It's become a fairly common occurrence in shops to be faced with a tubeless wheel that was doing fine, slowly started having issues, and hasn't had a sealant re-up in a while or ever, but what sealant was used is either lost information or one you don't have handy. If unknown, maybe you could figure it out if you pull the tire, but that's sometimes easier said than done these days, and you can always clean out what's in there and start over, but what you really want to do if possible is just shoot some fresh sealant into the valve and move on.
Every sealant manufacturers says not to mix brands, yet experience bears out that usually if you just do it, it's fine. But what possible exceptions are there, and why? Are there any sealants out there that are particularly bad for the purpose of possibly mixing with unknown prior sealants? Any that are particularly good? Any hidden compatibility rules that might allow a shop to responsibly only have a small number of bottles around yet still be able to handle anything that comes in the door?