Is there a way to use Series 1 Apple Watch for Basic Functions?

I don't think your problem is a universal one - it probably involves getting a new phone without transferring data from an older one.

I bought my Apple Watch Series 1 in March 2018 and connected it with my iPhone 6. Later that year, I got an iPhone 7 and transferred everything to the new phone and only seemed to lose a little workout data. Last summer, I transferred everything from the iPhone 7 to an iPhone 14. I currently am running WatchOS 6.3 on the watch and iOS 17.3.1 on the iPhone and have no issues syncing my watch. Of course, I have no idea if I could add a "new" Series 1 at this point.

Some apps that I was using have lost support on the watch (Zwift, HeartCast, etc.) due to requiring WatchOS 8 or higher.... and I did have to replace the battery on my own last year (it swelled and popped the screen off - I fixed it with a $16 battery and kit off of Amazon), but all Apple apps and most others (Fly Delta, SleepWatch, Strava, Pandora, etc.) still work.

Most people are shocked that my watch is a Series 1 and that it still works (doing Apple Maps navigation, Walkie Talkie, Messages, Workouts, Weather, Siri, Music, etc.) more than 7 years after being introduced in Sep. 2016.

If nothing else, I'd think you could pick up or borrow an older iPhone to sync it with.