I have received enthusiastic feedback from my new manager about my work and the way I have been running the team.
This is a Good Thing, but it doesn't count for very much unless it is written down somewhere (e.g. in your performance review, if your company does those). If you take written minutes of your meetings with your new manager, then that would suffice, assuming the praise is actually getting recorded there. If not, then you might want to send follow-ups of the form "As we discussed, Project X is moving along well, Project Y is blocked on issue Z, ..." via email. Then your new manager's lack of a reply serves as tacit acceptance of your version of events. However, if this is not a common practice at your place of work, then this might come across as weird or off-putting, so use your best judgment here.
If it's not in writing, then you should politely accept the praise, but assume that it's worthless from a career perspective, unless and until you see concrete rewards such as a raise, bonus, or promotion.
New manager mentioned that I will continue leading the team long-term, but didn't provide any clarity on whether this would be an informal arrangement as it is now (with me technically still in my lower level role but effectively running the team) or a formal one (me getting a proper promotion).
You should explicitly ask your new manager for clarity on that, as soon as is practical. Do not allow this extra responsibility to silently become "the new normal" for your job, unless they are willing to give you the raise and title to go with it. If they get evasive, make sure they know you are unhappy (assuming, of course, that you really are unhappy). Depending on how this conversation goes, it may also be a good idea to dust off your resume.
On the other hand, it's possible that they can't give you a straight answer right now, because they're still waiting to see what happens with your old manager. Nevertheless, you shouldn't allow them to stick your career in an indefinite holding pattern. If they don't know now, then they will probably know later. Ask them when they will have more information, and then ask follow-up questions when that date arrives.
New manager also mentioned that they want to reshape my old manager's role when they come back. New manager asked me to come up with a few proposals for what tasks we might give to old manager when they are back.
This sort of thing seems fairly standard to me. The new manager is trying to keep the bus factor from dropping too much while the old manager is away. Bear in mind, the person who actually ends up getting those tasks might or might not be your old manager, depending on whether they come back at all.
My old manager's leave was initially meant to last 2 months, but it keeps being extended with doctor notes. The latest update is that my old manager might come back in early June, but no certainty.
From what you said earlier ("late 2020"), your manager has now been gone for at least a solid four or five months, if not longer. This suggests to me that your old manager might not return. If they do, it might be in an entirely unrelated role. Therefore, you should assume that your current position is at least semi-permanent, and plan your career accordingly.
Old manager tried to contact me outside of work for a chat but I have been told by new manager and HR that I can’t communicate with old manager until he is back.
This is unusual, in my experience. Here are some (highly speculative!) possibilities that I can think of:
- Your old manager is in the process of leaving the company on bad terms (e.g. being fired, constructive dismissal, etc.). HR is afraid that your manager will try to cause problems if they talk to you.
- HR believes that the company will be held responsible if you "talk about work" with your old manager and cause them further stress or anxiety. This is not impossible; they've already had multiple doctor's notes!
- Some particularly weird brand of office politics is going on, and your old manager is at the wrong end of it.
Regardless of the specific reason, I would recommend caution here. Here are some things for you to consider:
- Talking to your old manager, in defiance of an explicit instruction not to, will (rightly or wrongly) be interpreted as insubordination, and can lead to various negative consequences if HR finds out about it.
- I've never heard of an employee being told not to talk to another employee outside of work, except in cases of harassment. But your old manager contacted you, so I doubt you are (credibly) accused of harassing them. (If you know that you have been accused of harassment, regardless of whether it is credible or not, then you should not talk to the person you are accused of harassing.)
- If HR is screwing over your old manager in some way, then it might be a good idea to find out more about the situation, to determine whether it could affect you or your team. Talking to the old manager is probably the most straightforward way of getting that information, but other coworkers might know about it as well.
- If you don't trust your old manager, then talking to them is probably not worth the risk.
- If your old manager no longer wants to talk, then the problem solves itself.
- If you have a union, talk to them and ask what they think of this.
- I would not recommend asking HR any follow-up questions. If answering those questions was in the company's best interests, they would have explained everything to you already.
Overall, I tend to lean against talking to your old manager, but you have a better understanding of the on-the-ground reality here, so you might come to a different conclusion than I did.