First things I can think of would be to check with any group that you have confidence of being the organizers and do some social media searching for Street Medic groups that might publicly operate in the area where the protests are to take place.

Ask about their needs for first aid or how to be included into whatever their First Aid or Street Medic people have going on.

If your assembled group is going it alone, easiest would be to move in small groups. Less big things to pack in/out, won't have to worry about police/counter protesters capturing/destroying stuff and can move quickly to follow protest movement.

If the protest is expected to be in one place an not move, one group can staff a fixed Aid point where you all can rest, move causalities to, resupply, and keep physical rally point when/if physical separation from your team happens.

Plan some things out ahead of time like meal/rest/resupply breaks, how you all are going to communicate when you have to move beyond line of sight, how long you all are going to operate, when or how you all will decide to disengage from aid operations, and how you are going to leave the protest area (try not to leave the area alone, try not to go directly to your vehicle, when you separate from your team call or send a text to confirm that they got home OK).

There are Street Medic Handbooks online all over the place, As you're already in healthcare, maybe this is pretty standard so maybe just a quick flip through might give you some ideas how Street Medics try to operate out in the wild.

Don't bring anything with you that you cannot afford to lose.

If you're wanting to be anonymous, find a resale shop like Goodwill or the Salvation Army or a Church resale shop and try to buy a disposable set of clothes, if you're lucky you can find a pair of comfy running shoes that can be trashed or re-donated. Don't reuse clothes/shoes if you're really concerned, consider them one use.

Typically symbol for medical aid is a white field with the red cross. Make some arm bands and a large patch to attach to your packs. A three foot of length of rigid PVC tubing .25 to .5 inches in diameter should be easy enough to attach to the side of a pack to make a flag that can stick up over crowds if your expecting a very crowded protest.

Don't bring expensive cell phones as a general rule. Either walkie talkies or cheapo phone card flip phones were you can keep the battery physically separated. Memorize all important numbers or preprogram them into your phone, a laminated note card kept in your pocket works as well. Only really needed when the area is large enough that you can't maintain verbal communications or when you expect to be separated.

Cheap wrist watch, digital.

Basic communication stuff. Don't use real names, if possible code names for people and places should be used until dealing with people outside of your group or emergency services. When possible, long conversations should be had in person, use the radios for emergency communications, check ins between people in your group, and calling one group to physically meet with the other group. I won't bore your with some basic army radio communication etiquette. I imagine that working in healthcare, you've got something like this already ingrained.

Use any satellite map program you normally use to get an idea of the topography of the area. If you're not planning on having a fixed Aid point, note places as rally points for when you get separated or need to take breaks. How will you get away from the area if things get too hot? If there is time, a casual walk through days in advance should be used to look for security cameras and to help the satellite maps make sense. Think about places to move casualties to, and where you will be able to hide from projectiles and stampeding people.

I'm sure I could think of more things but its late and the /tactics comm probably has a decent amount of stuff you might be able to find useful.