I just set up a local instance of Invidious. I created an account, exported my YouTube subscriptions, and imported them into Invidious. The first time I tried, it imported 5 subscriptions out of 50 or so. The second time I tried, it imported 9.
Thinking there might be a problem with the import function, I decided to manually add each subscription. Every time I click "Subscribe," the button will switch to "Unsubscribe," then immediately switch back to "Subscribe." If I look at my subscriptions, it was never added.
My first thought was a problem with the PostgreSQL database, but that wouldn't explain why some subscriptions work when I import them.
I tried rebooting the container, and it made no difference. I'm running Invidious in a Ubuntu 22.04 LXC container in Proxmox. I installed it manually (not with Docker). It has 100GB of HDD space, 4 CPU cores, and 8GB of memory.
I have ReVanced on my phone, STN on my TVs, and uBlock+SponsorBlock on my PCs. I was looking for an alternative that I could run on a server and would replace the various different apps I'm using. TubeArchivist ended up working perfectly for me; your mileage may vary.
Newpipe is a smartphone app, Invidious is a web frontend. I use the former but comparing the two are like apples and oranges. Clearly OP had their mind set on a web install.