What's a good replacement to the bookmark archiving service at https://bookmarks.google.com which will be shut down by Google in September?
I'd say it depends on usage of these archives.
I was very happy with XMarks solution back in 2018 (formerly known as Foxmarks that even dates back to 2006), however this one was used aside from archiving also for syncing these bookmarks across various devices (Firefox application only). I have not met anything similar since then.
If you are interested only in archiving solution, I am quite satisfied with RainDrop. It is stable since 2018 when I transferred all my archive there. You can tag items as well as organize in you own folder structure.
If you are able to invest some money, then I would definitely recommend BookmarkNinja, it is an ultimate tool to manage bookmarks.
Apart from these two, there are services that remind RainDrop but cover more areas like eLink or DropMark. Each is specific at its own, it really depends if you want to do something more with that archive of bookmarks.