You don’t need to check addons are up to date every time you run WoW, that is just something you’ve been conditioned into by having it done automatically since the addon managers became popular.
There’s no need to update addons continuously, they’ll either work or they won’t. If they stop working, or are causing other problems, I look for an update preferring original sources. So for AMR I get the addon from this website, if there isn’t a website I look at WoWI or Curse. Since the Overwolf drama a lot more addons are moving to Github, so I’ve got a couple from there recently.
@yellowfive might be able to sort out an API for the other clients to include the AMR addon directly, I’m not sure if there’s a simple way of contacting them and I know your plate is already quite full.
I know foxlit, author of Venture Plan, Opie and others, set something up for his addons which he hosts on his website. Unfortunately the popularity of Venture Plan caused a lot of feedback in his discord which, I suspect, led to him taking a break.
From what I gathered, reading the discussion on his discord, he set up a URL the addon managers could look at which would flag if there was a new version, there was additional talk about the way he chose to do them which they didn’t like but he was trying to keep the data use low. Even 1kb of data becomes large if it’s being requested millions of times a day!
Not sure how much you know about the history of the managers.
The first time it became an option was with www.wowace.com which was initially just a library system for addon developers which Kaelten made, it became so popular that it became financially unsustainable. Back then bandwidth costs were a major component of running a website, making a client which people would run every time they started WoW caused them a lot of trouble, so they had to sell to keep it alive. If you clicked on that link you might have noticed it’s branded curseforged now.
That morphed into the Curse client, there were a couple of others but none seemed as popular as the Curse one. Years later and Curse was Twitch which was had been bought by Amazon a few years earlier. Amazon did what most large businesses do and looked at the costs/benefit of what they’d bought and Curse/forged was not seen to be worth it so it was sold. This is where Overwolf came in, they were aware of the costs and thought they could monetise it and make a profit. I’m not sure they were expecting so much resentment from some of the WoW community but it’s certainly caused them more grief than they would have expected.
A lot of what I wrote above is from memory, I’ve never used any of the clients and no longer have a Curse account. During one of the merger/upgrades/rebrands my account stopped working and I no longer had access to the email account it was associated with. Now I just have a Bookmark folder with the addons I can only get from Curse. If you’re young you might not know what browser Bookmarks are!