"My team is not satisfied because I am slow and ask a lot" - your team has unrealistic expectations. My expectation of a graduate developer is that they have basically zero applicable development skills, and that they'll learn on the job. You say you have 3 years experience, but that is 3 years of study, not three years of actual industry experience, right? Even assuming you interned every year, I would not necessarily assume that having been of much use.

Then they'll say no to his request and he's lost nothing?

This could be very dependent on the nature of the work you're expected to be doing. If it's something where there's a long expected onboarding process the answer might be different to one where you're expected to be nearly fully productive from day one.

"I'm spending 7 hours a day in meetings" - with whom? The developers on your team? If it's not them, how are you managing them at all? And if it is them, you need to ask them what is stopping them from helping each other get unstuck.

Reading the original version of this question, I'd guess you're not a native English speaker - is this correct? And if so, are you communicating with your boss in English and is English your boss' native language? All of this might change how they view your messages.

"less meetings" absolutely could be part of a solution - especially if you're having meetings that could be emails or IM conversations, or attending meetings you don't actually need to be involved in

@Voo I have literally never required a doctors note for short term sick leave, across three companies in almost 15 years.

This answer has some generalisations which don't always apply. Stress is definitely a reason for taking sick leave in some organisations, especially in countries where the work-life balance is less tilted towards the interests of the employer (e.g. not the US). It is absolutely not a requirement that you have visited a psychiatrist to diagnose you with having mental health issues before you consider taking sick leave for mental health reasons in the UK.

"Your employment contract has to not outright forbid it" depending on location, this sort of clause may be unenforceable.

Can you explain how the severance works? Surely if he quits to take a new job, he isn't entitled to severance pay, so if he turns down whatever offer you make by going elsewhere, the severance is irrelevant? Are you likely to fire him/make him redundant under any conditions where the severance would come into play (the rest of your post makes that seem very unlikely)?