No. Modern SSDs are quite sophisticated in how they handle wear leveling and are, for the most part, black boxes.
SSDs maintain a mapping of logical blocks (what your OS sees) to physical blocks (where the data is physically stored on the flash chips). For instance, when your computer writes to the logical block address 100, the SSD might map that to a physical block address of 200 (this is a very simplified). If you overwrite logical block address 100 again, the SSD might write to physical block address 300 and remap it, while not touching the data at physical block address 200. This let’s you avoid wearing out a particular part of the flash memory and instead spread the load out. It also means that someone could potentially rip the flash chips off the SSD, read them directly, and see data you thought was overwritten.
You can’t just overwrite the entire SSD either because most SSDs overprovision, e.g. physically have more storage than they report. This is for wear leveling and increased life span of the SSD. If you overwrite the entire SSD, there may be physical flash that was not being overwritten. You can try overwriting the drive multiple times, but because SSDs are black boxes, you can’t be 100% sure how it handles wear leveling and that all the data was actually overwritten.
All video codecs are lossy, meaning you will lose some quality. AV1 and H.265 are modern video codecs with the best quality to bitrate ratios, meaning you can get better quality for the same bitrate, or the same quality with a lower bitrate. The downside the these codecs is that they are very complex and computational expensive to do in software. You’ll want to make sure your GPU supports hardware encoding for the codecs you intend to record with. The reason most people will recommend AV1 over H.265 is that AV1 is royalty free. With H.265, companies have to pay a royalty to use H.265. Because of this, most companies (Netflix, YouTube, Facebook, Twitch, etc.) want to use AV1 going forward, meaning in the near future, it will probably be the dominant codec.