As an update, I've configured gitmate in devguide and core-workflow repos as an experiment. I have not added it to CPython yet.
Disabling gitmate is as simple as one click.

I've made it to apply `status-stale` labels on pull requests, and `size-{XS,S,M,L,XL}` to pull requests.
 
When will we apply the stale label? 

The number of days can be configured. For now I've set it to apply the `status-stale` label if it has no activities after 60 days. 
Stale PRs in core-workflow and devguide:
https://github.com/python/core-workflow/pulls?q=is%3Aopen+is%3Apr+label%3Astatus-stale
https://github.com/python/devguide/pulls?q=is%3Aopen+is%3Apr+label%3Astatus-stale

PRs don't get automatically closed, but I would like for maintainers and bug triagers to go over PRs with such labels periodically, and either ask for an update, or make judgement to close them due to inactivity. Especially if a core dev has requested changes, but the PR author did not respond. 

Is there a way to apply it for
multiple reasons? For example, 1) PRs older than a year

Yes if people think 1 year is more reasonable than 2 months, then I can update it to 1 year.
 
2) PRs need rebase 

 There is an open PR [1] to detect this, sadly it is also stale  (waiting for me to review) 

3) PRs update Misc/NEWS

You mean if it is missing news file? We already have it as a status check, if would also like a  `needs misc/news` label, it won't be too difficult to do.

More and more PR look like a blinking christmas
tree :-) IMHO labels doesn't add much value for the reviews.

Thanks for sharing your point of view. I find labels useful, especially when needing to search for issues in specific categories.
For example, periodically I would go over all PRs that have the labels: `CLA not signed`, `needs backport to `, `awaiting merge`, `awaiting core review`.
Without labels like those I would have to go over each PR one by one.

It might seem more messy when viewing all PRs but I can live with it.
When reviewing an individual PR, the labels are on the right side and not interfering with the discussion on the left.

About the size labels, the idea is to quickly identify the size of the PR (based on number of lines changed), and people looking to help review PRs can use the labels to help decide which PR they want to review.
For example, when I know I don't have a lot of free time available, I'll be able to look for PRs with labels size-XS or size-S. When I have more free time, I can look into size-L PRs.
New contributors and new reviewers might be more comfortable reviewing size-XS and size-S PRs to start, and they can use the labels to filter PRs.
While smaller size PRs don't always not necessarily mean easier decision making time, but sometimes it can be a good indication.

Mariatta