Thanks for posting the screenshots, I think this is a certificate issue.
This arises because when you access your NAS via its Tailscale IP, your regular certificate tied to your domain name no longer matches the IP address you are using to access your NAS. This is why you get some certificate warnings.
Try again to connect to your Tailscale IP via safari on your iPhone, at
https://tailscaleip:port. This will generate a “This Connection Is Not Private” warning. Tap Show Details, then visit this website to override the warning. Success here will confirm that you can access DSM through Safari.
If this still doesn’t work, you could try connecting to DSM at
http://tailscaleip:httpport. This port number is usually one lower than the https port number.
Once you’ve confirmed you can access DSM using either method above, then focus on Drive app.
Drive app on your iPhone may not be able to connect because of the certificate issue when accessing via Tailscale IP. To overcome this, disable HTTPS in the Drive app, and try connecting to the Tailscale IP, but use your DSM’s http port number as above.
Using Drive app to connect via HTTPS with certificate validation won’t work as you are accessing at TailscaleIP not https://name.dnshost.com.
Tap the settings button in the bottom left of the Drive app and see if you can add the TailscaleIP as a trusted host. I’m not too familiar with Drive app so not sure how this is done, but once your TailscaleIP is “trusted”, you maybe able to connect using HTTPS from Drive app.