If you ever worked in an agile team and used SCRUM you probably heard of Definition of Done. While I am still skeptical that SCRUM is the best way to build a product, I find having a Definition of Done to be really helpful.
Here are some things I find to be valuable to have in there when it comes to testing.
1) Tests on devices/browsers listed in the project assumptions passed
What devices and browsers you should test depends on your product, your market and many other factors. You should, however, have a least one low-end Android device in there, like the Moto G4 or the Alacatel 1X. Testing there gives you a good idea how efficient a feature really is.
2) Can be used with keyboard only
That's self-explanatory – all actions of the feature can be done by using only your keyboard.
3) Automated accessibility tests passed
While you can't automatically test any accessibility issue, it is a good start. There are various tools available, like WAVE, axe, Pa11y and many others. Most tools show you contrast failures, missing alt attributes, missing labels and much more.
4) Test with screen reader passed
You should at least test with one screen reader. You can use a free screen reader like VoiceOver (macOS, iOS), TalkBAck (Android), NVDA (Windows) to test. Note, there are differences between screen reader, how they support web features.
This list is by no means complete. Nothing will ever be perfect, but if all these tests pass you are most probably ready to ship.