Pulled up for “picking on someone at work”.

Yes, but you peers are either not "mature enough" to do the same or haven't been given any guidance/training on how to do their job. So at what point the management is willing to get involved?

Well you should be mature enough, but clearly you lack the skills to communicate effectively.

who told you you were effectively bullying? And what does lost it look like?

Stop clearing up the office - put up a rota for it

Stop doing their work - just say "xxx is doing that , please get the output from them "

Who informed you that you had been accused of picking on people? How did you reply to them?

If they are management, this would have been the perfect time to escalate the matter calmly and professionally- you've tried to manage it yourselves as requested and that hasn't worked.

If management still do nothing, arrange a strategic overlap of holiday and sudden sickness with your colleague who actually works, ideally when there is a (minor) deadline involved. Sadly sometimes such action is needed to get management to pay attention.

I think a meeting is called for with management

Op, surely you cannot be this ignorant of how to behave in a workplace?

the strategy is

if you have concerns about any colleagues, speak to your supervisor.
do not gang up with another colleague to have an assertive word.
do not lose it,walk away and sit somewhere if you cannot control yourself
hope like fuck you’re not going to get accused of bullying, as quite frankly this complain would be upheld

Cross post! Good luck getting it sorted, OP.

She's not saying she's not going to do her job. She's saying she wants to avoid being in the position she was in before, of doing her job and part of other people's jobs too. It could have been expressed more clearly, I agree.

Presumably you have documented these 'chats' and given copies to both HR and the people concerned themselves?
Assuming you and your other colleague are also the managers of these people? Otherwise, you are both completely out of order. If you and your colleague are at the same level as these 'work-shy' bods, you should have spoken to their manager, not taken it upon yourselves to try and deal with them.
However, if you are their manager, then you should be disciplined for ineffective management; losing one's temper like that is never acceptable. If you aren't their manager, you should be disciplined for not following proper processes for dealing with slackers (grievance, etc)
Either way, you have not covered yourself in glory. If it were me, I'd be mortified

I haven't any tips but our workplace is spit between 2 who do and 2 who don't.
Nothing has changed after raising with the boss as they don't want to lose any staff and those who do are the least likely to leave!
It's whoever sets expectations fault for not reinforcing their roles etc..its not pleasant and builds resentment.
Have you got people higher up to support you or are they making it your problem?

Unless you are their line manager, I am not sure it is your place to comment on their work. If you don't receive handovers and it prevents you from doing your own work, you can request one in an email and copy in the line manager or whatever is the procedure at your place. Continue until something is done about it. Do not do the work for them. If asked, say you are at capacity.
Difficult to advice without knowing what your job entails.
As to cups, same thing. Have your own in your desk drawer, don't wash up theirs.

How exactly did you lose it?

WIBU to expect colleagues to do their share? After all, it’s the rest of us that end up picking up the slack.

You know this isn't UR.

Also, I really want to go back to work with a strategy that involves me not doing my job, and in addition picking up the slack for others. Any tips?

This is immensely childish. Don't do this or you lose any moral high ground you've currently got. Focus on the evidence supporting their lack of effort.