O3s work too well? Team Lead's responsibilities are quadrupled.

I keep the sizes of the teams that my leads manage down to four.  My rationale is that I want to make sure that my team leads are still practitioners in their field, rather than becoming full-time managers.  Even for a "full-time manager", though, anything above about 7-8 people just isn't workable.  You've still got work of your own to do, and keeping track of the deliverables for 20 people is a real handful.  A quarter of your working week being taken up with one-on-ones is a significant load, too.

I think it's probably time for a discussion with your boss about appropriate team sizes.  Mention that one of the reasons you've done so well so far is that you've been able to provide individual attention and guidance, and with 20 people that is likely to be reduced.  Offer to help guide others in the MT ways, and grow more team leads to work alongside you (or under you).

If your boss isn't receptive, and you're definitely going to be leading 20 people directly, you've got a few options.

If you've got a certain amount of independence, you can consider blessing a few unofficial team leads.  Find out which of your people are interested in future leadership opportunities, and delegate some of the leadership duties to them.  You probably can't give them pay rises, or official titles, but the best people aren't motivated by those things anyway.  The opportunity for a little more responsibility and learning a lot of new stuff may well be more than enough to get some people on board.  Don't select based on seniority, that's a recipe for disaster; explain the situation and ask for volunteers.  It's worked amazingly well for me.

On the other hand, you're probably in an environment where those sorts of unofficial shenanigans won't go over at all well.  In that case, you've just got to up your game to stratospheric levels and keep rocking.  Keep your O3s tight and efficient.  You will need to become an expert in the taking of notes and the organising of action items and things to followup.  If you're already a devotee of Getting Things Done, Action Method, or a similar way of organising the things you have to do, now is the time to start learning -- because if you're disorganised, the extra pressure of having 20 people on your mind will cause a meltdown quicker than a Japanese earthquake.  It's not impossible, though -- plenty of people have managed it.  You'll certainly learn plenty of neat tricks that will serve you well throughout the rest of your career.

Congratulations on your progress!

You are responsible now for the effectiveness of the twenty of you, including yourself.  That requires you organize them to suit the new situation, and to let everyone learn (including yourself) how to operate well within that.  At 20 people, the "head" person really needs to focus on managing -- any non-management work by that person will be incidental, and should be kept as an "emergency reserve" if not ignored outright.  From your description, you've been given the "head person" assignment.  Confer with your manager for context and constraints.

Seems to me that if everyone is currently doing very similar work, you can best honor the situation and responsibilities by pulling in four or five volunteers to grow into team lead roles, and spreading the rest across the team leads to form relevant teams.  You can say it's an experiment, to make it easy for team-leads-in-training to swap roles with individual contributors, and use the results in several months to help press for appropriate rewards for all involved.  Of course, you'll be coaching your team-leads in how to be effective team-leads, including how to use O3's.

You will have some interesting dynamics to navigate along the way.  You will be learning to exceed the capabilities of your "supervisor" and match those of your manager, most likely -- unless you hand over some of your twenty to the supervisor, swap seats with your supervisor and become *his* manager, or in some other way help restructure more of your department than just your twenty.  I'd suggest that's reason enough to sit down with your manager and the department head to work out how to place people and roles.  You'll need to do this anyway towards year-end, might as well work it out now in preparing the transition to having twenty people "in your team".

Good luck and may you continue to do well!