Congratulations, you seem to have won the "great employee" lottery.

Bob is becoming somewhat anxious, as he feels guilty for not having enough tasks and is getting increasingly worried that our manager might be holding tasks from him in so he can fired

This is a simple communication problem. Your manager (and maybe you, depending what your role is) need to tell him repeatedly that he is great and that there is zero intention to fire him. Actions are good too: a raise or public recognition go a long way in adding credibility.

as we simply can't separate tasks quickly enough to keep his queue going -

That's where your problem is: poor planning. It's actually quite rare that a dev team has an empty backlog. A few things you can do

1. Spend a little more time grooming and filling the backlog. If you ae doing scrum, make sure that your backlog has 2-3 sprints of work in it.
2. Do some strategic planning. Are there any high level projects or architectures that Bob could work on. What things may you need in 3 years from now that are not on the daily task list.
3. It's a good idea for everyone (including Bob) to have a well defined side or pet project. Something that's useful for the business, fun to do, but doesn't have a hard deadline or deliverable yet. Could be technical or scientific research, tools, process improvement, experimental features, documentation, user research, competitive analysis, etc. This is "stuff to work on" if your hair isn't on fire and your tasks are mostly done. These can be defined in collaboration between the employees and the business stakeholders.
4. Ask Bob what he wants to work on. What ideas does he have that are fun for him and also good for the business.

Honestly, it shouldn't be too hard to keep Bob's plate full. Most managers would give their left kidney for that type of employee. If your manager is "too busy" they are not prioritizing correctly.

Congratulations, you seem to have won the "great employee" lottery.

Bob is becoming somewhat anxious, as he feels guilty for not having enough tasks and is getting increasingly worried that our manager might be holding tasks from him in so he can fired

This is a simple communication problem. Your manager (and maybe you, depending what your role is) need to tell him repeatedly that he is great and that there is zero intention to fire him. Actions are good too: A raise or public recognition go a long way in adding credibility.

as we simply can't separate tasks quickly enough to keep his queue going -

That's where your problem is: Poor planning. It's actually quite rare that a dev team has an empty backlog. A few things you can do

1. Spend a little more time grooming and filling the backlog. If you are doing scrum, make sure that your backlog has 2-3 sprints of work in it.
2. Do some strategic planning. Are there any high level projects or architectures that Bob could work on? What things may you need in 3 years from now that are not on the daily task list?
3. It's a good idea for everyone (including Bob) to have a well defined side or pet project. Something that's useful for the business, fun to do, but doesn't have a hard deadline or deliverable yet. Could be technical or scientific research, tools, process improvement, experimental features, documentation, user research, competitive analysis, etc. This is "stuff to work on" if your hair isn't on fire and your tasks are mostly done. These can be defined in collaboration between the employees and the business stakeholders.
4. Ask Bob what he wants to work on. What ideas does he have that are fun for him and also good for the business?

Honestly, it shouldn't be too hard to keep Bob's plate full. Most managers would give their left kidney for that type of employee. If your manager is "too busy" they are not prioritizing correctly.

Congratulations, you seem to have one the "great employee" lottery.

Bob is becoming somewhat anxious, as he feels guilty for not having enough tasks and is getting increasingly worried that our manager might be holding tasks from him in so he can fired

This is a simple communication problem. Your manager (and maybe you, depending what your role is) need to tell him repeatedly that he is great and that there is zero intention to fire him. Actions are good too: a raise or public recognition go a long way in adding credibility.

as we simply can't separate tasks quickly enough to keep his queue going -

That's where your problem is: poor planning. It's actually quite rare that a dev team has an empty backlog. A few things you can do

1. Spend a little more time grooming and filling the backlog. If you ae doing scrum, make sure that your backlog has 2-3 sprints of work in it.
2. Do some strategic planning. Are there any high level projects or architectures that Bob could work on. What things may you need in 3 years from now that are not on the daily task list.
3. It's a good idea for everyone (including Bob) to have a well defined side or pet project. Something that's useful for the business, fun to do, but doesn't have a hard deadline or deliverable yet. Could be technical or scientific research, tools, process improvement, experimental features, documentation, user research, competitive analysis, etc. This is "stuff to work on" if your hair isn't on fire and your tasks are mostly done. These can be defined in collaboration between the employees and the business stakeholders.
4. Ask Bob what he wants to work on. What ideas does he have that are fun for him and also good for the business.

Honestly, it shouldn't be too hard to keep Bob's plate full. Most managers would give their left kidney for that type of employee. If your manager is "too busy" they are not prioritizing correctly.

Congratulations, you seem to have won the "great employee" lottery.

Bob is becoming somewhat anxious, as he feels guilty for not having enough tasks and is getting increasingly worried that our manager might be holding tasks from him in so he can fired

This is a simple communication problem. Your manager (and maybe you, depending what your role is) need to tell him repeatedly that he is great and that there is zero intention to fire him. Actions are good too: a raise or public recognition go a long way in adding credibility.

as we simply can't separate tasks quickly enough to keep his queue going -

That's where your problem is: poor planning. It's actually quite rare that a dev team has an empty backlog. A few things you can do

1. Spend a little more time grooming and filling the backlog. If you ae doing scrum, make sure that your backlog has 2-3 sprints of work in it.
2. Do some strategic planning. Are there any high level projects or architectures that Bob could work on. What things may you need in 3 years from now that are not on the daily task list.
3. It's a good idea for everyone (including Bob) to have a well defined side or pet project. Something that's useful for the business, fun to do, but doesn't have a hard deadline or deliverable yet. Could be technical or scientific research, tools, process improvement, experimental features, documentation, user research, competitive analysis, etc. This is "stuff to work on" if your hair isn't on fire and your tasks are mostly done. These can be defined in collaboration between the employees and the business stakeholders.
4. Ask Bob what he wants to work on. What ideas does he have that are fun for him and also good for the business.

Honestly, it shouldn't be too hard to keep Bob's plate full. Most managers would give their left kidney for that type of employee. If your manager is "too busy" they are not prioritizing correctly.