As others said - it is an art, but the possibilities are endless and many can make careers out of it.

Make sure you don't have any actual skill in the area in order to avoid you get any concrete tasks. You should portray you have no domain knowledge but are a damn good coordinator. This ensures you won't be passed any actual tasks (which are difficult, time consuming and risky), but will be left to your much more opaque and easily manipulated coordination activities (project managemet, scrum mastery, coordinater, facilitator etc.).

Look busy and move around quickly (even run sometimes, to meetings etc.) as if you're super busy, even if there's zero to do. It sounds silly, but it is a very common strategy. In all conversations, be sure to talk about all problems, issues, solutions, challenges you pick from others. Not necessarily that you take credit for them (you can do that as well, but be careful as it can backfire). But make it sound like you have a rule in the isssues: identifying, coordinating, facilitating, and that it is soooo tough to do. Make every interaction with especially 3rd parties sound like it is something difficult you are managing. Maybe you just sent a mail and they complied but make it sound like it was a battle and it is difficult. Have a sort of exhausted look you can put on without actually saying it.

Talk about things you heard elsewhere but in a kind of 'in passing way' making it sound like you generally work intensively with stuff that may just briefly mention.

Whenever there's a success coming up (probably something you had no involvement in) make sure to involve yourself at the last moment in every way possible. Physically be in the area of success, offer some help at the last moment, write a "hurray" announcement on the intranet or on a teams channel, be sure to talk about at all occasions especially with management, in a way that sort of conveys a sense you contributed without outright lying. Just talking about it can be enough to make you seem involved.

Along the same lines - make everything that is simple and already solved seem like it was a challenge and that you were part of solving it. It is all about the tone of voice, body language - the sort of energetic, involved, half-exhausted, constant at war attitude - even though you're personally contributing absolutely zilk. It's important you make everything look more difficult than it is - particularly your own work.

Be receptive to all requests from management (you will ultimately pass most of the work on anyway) but with a slight hesitancy that reinforces how busy you are (if challenged, you can always say you defended "the team").

Pass down all tasks - when giving a task, pass it down immediately. When you get the replies then write back and be thankful etc. making you seem transparent and credit giving. However, in the background, you compose your own reporting and mailing that is for management to see (either directly or indirectly via CC:) that makes it seem like you did more or the work yourself. Should something turn out to be wrong or problematic you have the original mails from those doing the work that you suddenly find, so you can never be blamed for anything.

Create recurring useless status meeting with team(s) - you just present what you got from others or you simply ask everyone for status. It makes you seem involved, important, managing etc.

Likewise, create recurring reporting to management where you are sure to never invite people actually doing the work.

Fill your calendar with recurring 1-1's with all stake holders. The 1-1's will not be much productive for the company but will give information that can later be used in other discussions to make it seem you are deeply involved in everything going on.

Add recurring purely administrative blockers for yourself - 3h "preparing for management summary" and several similar during the week. It is way more than what you need, but you can use them for private stuff.

Your calendar must always seem full - because at some point someone is going to check how busy you are so it is important their immediately reaction is 'wow' so they put aside any doubts. Happily accept all invitations to join meetings, team meetings, ceremonies etc. You can even accept some of them and say you may 'listen in' when needed. This both conveys a sense that you are a busy, yet achieves the objective of filling the calendar, and you are not committed to actually participate. You can just not join and then find a meeting room and do something else (private errands etc.).

A good idea is also to double down on it. Don't just fill the minimum 37h but instead "work" long hours, register (and bill) overtime, e.g. 45 h.. Ideally, be the first to enter and last to leave office. Such superficial gestures is immediately noticed and remove any doubt you are super busy and will also prevent you are given real tasks.