What you have there is called an M.2 SSD specifically one using the NVMe interface.
You can get SATA inteface drives for M.2 as well, but you do need to check the motherboard supports M.2 SATA before buying one to replace it - In a laptop that's not a guarantee.
As for the empty 2.5"drive bay on the other side of the battery, I don't think so. It looks like they've stripped the SATA connector off the board to save a few pennies:
View attachment 162763
Personally, given that it's a cheap plastic laptop and everything is working fine (despite the temperatures and health being lower than expected) I'd just make sure I had regular backups and keep using it normally.
If you really want to replace the SSD, search for PCI Express M.2 2280 SSDs, and if the shop you're searching on has the filter, look for TLC not QLC as it'll run a bit cooler and faster.
In Europe, the Crucial P1 or Intel 660P are aggresively-priced models at 500GB or 1TB capacities; I think they'll be ample for this laptop.
If you want TLC instead of QLC then the WD Blue SN550 and ADATA SX8200 Pro are usually good bets for 10-15% more money.