Depends on how prescriptive you want it to be. Plenty of free form types where you can log all your stuff.

If you’re looking for a program, for strength training I recommend Mark Rippetoe’s Starting Strength. They made an app for it now, too. It’s a one-time purchase, includes an interactive copy of the book, and is ad-free. I’m a fan.

My preferred app (Fit Notes) is Android only and doesn't have any of the fancy features you mention.

My second favorite app (Personal Training Coach) does appear to be on Apple and has lots more features. You can pick between many popular lifting programs or setup your own. Programs can be built with progression plans and timers and can increase weight after a successful session, hold weights if you are unable to complete a progression, or reduce weight after multiple failed attempts.

Strong is fantastic, especially its Watch integration.

Hevy is often touted as being better, but I don’t like it. It has a strong social media hook and I don’t want that from a fitness app. I also never tried it on Watch, if it even supports it.

I use strengthlog, the free version is pretty complete and without ads

Streaks Workout

Easy, intuitive, purchase once :)

I use “Pumped” and it’s pretty great - and free.

https://apps.apple.com/au/app/pumped-workout-tracker-gym-log/id6474732457

I use Apple fitness app and the notes app lol

StrongLifts

Boostcamp does that, and gives some access to predefined workout programs as well.

Fitbod.

Apple Fitness+ has a custom plan thing. Not sure how good it is though.