Openstreetmap

You can use the various desktop and mobile clients to add details to areas outside of where you live, even if it's just adding buildings from the aerial views.

As far as Street Complete goes, you can save it for specific mapping days, and go somewhere just to map it. There will still be a record of where you were, but it will be generic. e.g. If you visited Bristol for the day and did a load of mapping, that's not going to reflect your day to day life, or any part of the day that you didn't map 👍

Street complete probably isn't the tool you want if you want to preserve privacy like this, people will be able to know where you have been. There is an option to turn off automatic uploads of answers however that will allow you to wait until a time you're happy to submit your changes, but this does increase the chance of change collisions.

A better workflow may be to just take notes with a GPS enabled voice notes tool, or similar and updating the map with one of the standard editors (ID etc) when you're back home.

You can make it anonymous by creating an account with a different username that you don't use anywhere else and a burner e-mail via SimpleLogin or AnonAddy or 10minutemail. Maybe also a VPN? And in the case of StreetComplete, uploading changesets manually at random times.

There's no way to not make a public trail, that's just how mapping works, but you can make it really hard to trace back to you. You also have to understand that no surveillance capitalism is at play here, there's no actor that will consume this data and use it to feed you ads or content.