USB 3.0 is 4 Gbps of data. Your adapter is 1920x1080x60Hzx24bpp = 2.99 Gbps so I suppose it could be lossless but usually there's some compression involved.
Anyway, since there's no macOS driver, your adapter will only work in Boot Camp. If you really want to use video from USB, then you should try a DisplayLink adapter which does have macOS drivers.
https://www.displaylink.com
To connect your Thunderbolt SSD and a display to your MacBook Pro (which only has one Thunderbolt 1 port), you should connect a Thunderbolt 3 dock using an Apple Thunderbolt 3 to Thunderbolt 2 adapter and a Thunderbolt 2 cable. A Thunderbolt 4 dock/hub is not an option unless you can get Big Sur installed. You could try a Thunderbolt 2 dock so that you don't need a second Thunderbolt 3 to Thunderbolt adapter to connect your Thunderbolt SSD enclosure but a Thunderbolt 3 dock has more features and is more future proof for when you decide to upgrade the Mac.
Which Thunderbolt SSD enclosure do you have?
There are some Thunderbolt 3 SSD enclosures that include a DisplayPort output and/or a second Thunderbolt port which can connect a DisplayPort display/adapter. So you wouldn't need a dock.
A Thunderbolt 3 dock or enclosure can add USB 3.1 gen 2 support (10 Gbps), so you could try a USB 10 Gbps to NVMe enclosure which are more portable and faster than a 2.5" SSD enclosure. I'm not sure it will be bootable from a Thunderbolt 1 Mac unless it's connected to a USB 3.0 port?
Thunderbolt 1 is limited to 10 Gbps but it has two channels so it basically has the same bandwidth as Thunderbolt 2 except the channels cannot be combined like they are in Thunderbolt 2/3/4. I am hoping that the display will use one channel and the SSD will use the other channel. I suppose you can verify this by testing the bandwidth of the SSD (if the SSD can use high enough bandwidth to be affected by the bandwidth used by the display).
What display are you connecting? A 1080p display only requires 3 Gbps, and your SSD is probably only 6 Gbps (4.8 Gbps of data), so they can both fit inside a single Thunderbolt 1 channel. So this is not a good test of multi channel functionality. A better test would be a 2560x1600 60Hz display (6 Gbps) (or 4K 30Hz display if you can somehow enable that resolution) and a USB to NVMe enclosure (10 Gbps). A display connected via Thunderbolt mostly only affects write speed so even if only one Thunderbolt channel was being used, the SSD would still have full read performance.