IME Micro-management is awful and can cause more rapid burn--out than even the huge work volume I experience at various pinch-points during the year. She's asked you to relay specific issues, so if you can, I'd respond with concrete examples. But the way these issues have been put to you sound less than professional. It's possible some are legitimate, but consider the way they've been put to you.
It had been noticed by people I wasn’t doing any work
If your LM has concerns then this is something you'd expect to be raised as a performance issue with supportive solutions, not to be made a target of office gossip. Perhaps be ready with some outputs so as to refute this point. You've offered a solution: more space to complete work and less time on phone calls and meetings. Do they have a response to that request to make those demands reasonable and workable?
It wasn’t obvious what I am doing all day
They don’t think I really have any work to do
The second point is merely a repetition of the first. Who is 'they?' Is this to be a recounting of office complaints, or a productive meeting to ensure requirements can reasonably be met? Why is the LM more interested in what other staff members are saying, rather than offering her own specifics as to what the issues are and discussing viable solutions?
I am distracted and uncontactable
Perhaps the volume of meetings, email and phone contact is an issue. Again, what would LM posit as a reasonable compromise?
They never WFH and are always visible
I don't see what relevance that has to you personally. It's none of your concern what others are doing; that's for management to deal with.
They are picking up all my slack and protecting me from work I should be doing as I keep saying I am stressed.
It's the LM's job to delegate work ensuring parity across the team. If you are not keeping up what you're given then this needs to be a conversation between the two of you rather than unhelpful comparisons between you and your colleagues. It's not a punishable offence to be 'stressed', but I'd recommend keeping your communication with these people and any complaints to a minimum. What you don't say, they can't use against you.
I need to give them a list of all the jobs I should be doing for them to compare with
Who is 'them?' You're expected to answer to your colleagues? No. You answer to your LM. Is she making it a requirement that you do this? If so, tell her you want the request sent to you in writing. If she does so, you'll have to comply, but if she's compelled to put it into a email she a) might not do so, knowing ow it could make her look and b) it could support a future case for constructive dismissal, if it's transpiring you are being treated differently and that this is being done outside any problem resolution framework.
I am too sensitive
I get over involved in trivial matters
I need to learn to not care about things as much
Here's where alarm bells ring for me: this is the language of a bully, and anyone who's ever one will instantly recognise it. Don't respond to those statements, simply say 'let's keep this professional and related to work only, as I'm experiencing this as personal criticism'. Likewise, you don't want to hear about others' gossip about you. If she has concerns about your performance then she's to address these directly with you, and you'll work on it with her. Comparisons with others are not your concern.
I disagree with you, OP, that your LM has given a 'specific' list. None of this stuff is specific. It's a litany of complaints and second-hand gossip which gives you nothing concrete to work with. I would, however, (quietly, and without admitting to it) take the second point under advisement. Let the trivia go, try to tune out the small stuff, and stop the complaints about the burn-out. It's gaining you no sympathy and is being used as ammunition against you. Withdraw. The best way to deal with that kind of environment is head down, mouth shut. If the office gossips complain about you, remember that what others think of you is none of your business.
You might also want to consider keeping a diary in a non-spiral-bound notebook with dates and times.
I get that this is not a pleasant way to live your working life. If it's a viable option I'd be thinking about moving on.