I was first a Instapaper user. I really liked Instapaper, but when they couldn’t comply with the then-new EU privacy regulations (“GDPR”) I left them (it’s really crappy to cut off basically a continent from your app, and especially crappy when that reason is data harvesting, something you shouldn’t have been doing in your reading app anyway).
I switched to Pocket then, who IIRC didn’t even have to change their policies for GDPR since they weren’t misusing private data anyway. It’s fine as a “save links to read later” system but like you I find it’s “management” facilities a little underwhelming. (To be fair I could probably have tagged a lot more, but it’s just more work 
)
In the last month I’ve switched to Readwise’s beta of Reader, their new reading app. That has tagging too, which I am once again ignoring, but actually the lack of sorting to me feels less overwhelming than it did in Pocket. I like that it separates items you’ve added recently from older stuff (called “inbox” and “later”) so you aren’t confronted with a giant list of articles you’ve failed to read when you open the app).
It’s also game-changing that you can save other stuff in there - it handles a lot including PDFs. I haven’t used that yet, but I’ve started forwarding newsletters to it so I don’t have them cluttering up my inbox. That is soooo good!
Also, I know it sounds ridiculous (I was very cynical!), but the listen function is great! I have some articles that are estimated reading times of over 30 mins. I figured I’d give the function a go since it’s there, and put a long-form article on to listen to while cooking. It’s really good! I wouldn’t do it for something I wanted to focus on, but they point out it’s really for “high volume low value” articles that you want to read but don’t expect to get much out of, and it’s great for that. I am finally starting to clear that backlog of articles that seem interesting but are very low priority so never get looked at! I have set up filters (called “views” in Reader) to identify articles with a long reading time, and I also created a tag for ones I think will be good for audio while I’m doing other things. Game changer.
Some of this will just be “shiny new app syndrome”, but I feel I’m clearing articles I save a lot quicker now with Reader than I did with Pocket. It helps that emails are now in the same app so I don’t have to hesitate over whether to open Pocket or open email to catch up with newsletters. Being able to highlight stuff and quickly export it wasn’t a major priority for me, but it also made that bit of my life easier. I can highlight an article, export the highlights as markdown, and the job’s done!
I am going to keep Pocket. I don’t want to save in Reader websites that I’m saving that I just want to look at (as opposed to read) - I did both in Pocket. My plan now is to use Pocket just to save websites I want to explore in more detail, and use Reader for specific pages and emails I want to read.
! I’ve tried all the newbies. Instapaper is still the best.