Took on a client last year who is on squarespace and refuses to move, so I have had google search console for squarespace running for about six months now. Verification is the easy part, there is a field in the settings for the verification code and it just works, no dns records, no file upload.
What it has been worth having:
1- it found that squarespace was generating two urls for every blog post, one under the blog path and one under the tag path, and both were indexed
2- the query data, which is the only place you see what people typed, since squarespaces own analytics only shows you traffic sources
3- the core web vitals report, which is the only leverage I have that makes the client stop adding full width video headers
What it cannot help with is anything you would then want to change. You cant edit robots.txt on squarespace, redirects are limited to their url mappings panel, and the sitemap is whatever they decide it is that month. The reports end up describing problems nobody is allowed to fix, and that gets old fast.
For traffic numbers next to it I have GA4 plus something lighter the client can actually read, and I have tried three, plausible, fathom and devdome. The last of those reports fine and the bot filtering saved me an argument about a traffic spike, but it is built wordpress first, so on squarespace you are pasting a script tag with none of the plugin side, which is half of what you pay for.
The client has not opened any of it since March.
Source: r/WebsiteInsights · by /u/Girafffe55