Officially they said it's because most likely everyone will have previous charge brick so they are reducing materials etc. True, but for me I have an S10 fast charge brick which will either take ages or not charge my S21 ultra at all. I've had to buy a 15w charger frustratingly.
Your S10 charger should charge it just fine. "fast charging" ( or around 10-18watt ) is often disabled out the box, if you haven't ensured it is enabled already, Settings > Battery & Device Care > Battery > More Battery Settings- and toggle fast charging on.
yes, as long as it's type c on one end, which it is, it will charge your phone, and I think I remember a type c to c 25 watt charger on the S10 5G, and maybe even on S10+/S10 etc, if not they will be at least 15 watt, so either way, it is the same charger that the newest models support, whether that be 15 or 25 watt. it's always good to have a spare though, if you keep the one you already bought.
If you have a S10 charger it will work. Just have to enable fast charging. Out of the box the S21 only has charging and super fast charging enabled. To be honest having tried fast and super fast charging the over all charging time is only reduced by maybe 10-15 mins. So unless that's a big issue for you I would stick with the charger you already have.