Add memory to 2013 (trashcan) Mac Pro

I really think you mean storage, not memory An SSD is storage.

Yes, you can use a standard NVME SSD with a simple adopter.

I use this adopter

https://www.amazon.com/gp/product/B01CWWAENG/ref=ppx_yo_dt_b_asin_title_o05_s00?ie=UTF8&psc=1

with a standard NVME SSD. The Evo 970Pros do not work. I think I have the standar EVO 970. I have been using it since 2019 when a firmware update to the trashcan allowed the use of NVME SSDs.

Yes. Check Other World Computing's site macsales.com.

OWC/MacSales many upgrades available for the 2013 Mac Pro. I've upgraded the SSD, memory & processor in my 2013 Mac Pro.