You can use Service Tokens with Cloudflare Zero Trust (Access). Unfortunately, the companion App then has to support setting custom request headers, in order to send the token. Not many support this in my experience.
The only other option would be to use Basic Authentication, instead of Cloudflare Access. This isn’t as secure, but would be supported by most Apps (since you can simply inline user:password in the API URL). You can even setup a Cloudflare Worker to add basic auth to any Route you want.
Ideally, would love some hybrid of these approaches, where I can keep Access enabled, but override with basic auth for ‘legacy’ apps. Don’t know of a way to do this though.
Edit: Forgot to mention a third option, if you just want access while home, you can setup a bypass in Cloudflare Access policies for your home IP address. Then if you really need access when remote, you could also use VPN, but not as seamless of course.