How can I tell if a site is being rate limited?

I don't have personal experience using it, but I believe Ooni Probe is designed for your exact use-case:

https://ooni.org/about/

Just curious -- if a country didn't want a site to be seen, why would they rate-limit it instead of just blocking connections completely?

Is that a thing countries do, like if they want to "punish" a site while retaining plausible deniability?

Have some fun at the same time: 1) get a vpn account (proton, other) 2) hack your worst enemy's wifi with your favourite tools 3) while outside your enemy's home, boot a linux live distro 4) change your computer's name to your enemy's name 5) connect to the enemy's wifi 6) try to visit all the sites banned by your country 7) insult your country's leader in a public forum using your enemy's name 8) test the speed of the suspected rate-limited site 9) set-up your vpn account settings 10) using your vpn, re-test the rate-limited site 11) subtracting a fair percentage slow down because of the vpn, gauge if there's a significant difference between the two tests 12) turn off computer, go home, enjoy tasty beverage 13) grab some popcorn, go watch your enemy's house from a reasonable distance 14) post video on youtube of your enemy getting busted, using your favourite heading

If that's all too much fun for you, then skip most of it and only do #s 8 to 11 from your own network or favourite hot-spot.

The thing about rate limits is, there are often hard limits. Try querying the site a bunch and see what the data transfer rate is. if it's consistently incapable of going above say, 128K/sec, you've got your rate limit.

Other times, they'll allow for bursts but sustained get rate limited - these can be detected just the same depending on their approach; if it's per connection (and not IP) you may have to find a big file to download.

It also helps to establish that traffic to other sites is not rate limited, and to use 3rd party checkers that check for connection rate across the globe. Or DIY and spin up a bunch of EC2 machines that are geographically diverse.

My country used to heavily censor internet pages, do finishing attacks on Facebook, Gmail etc..

The easiest way to prove it is by using a VPN or a proxy. Check with different ISPs, also try mobile vs home.

I can definitely notice an improvement in performance when I use a VPN, however it would be cool to see where things are being delayed. Is traceroute or curl something that could help here?

One possible method: Write a script to request the site continuously and see if it fails to respond with any regularity. From there you can start dialing it in and determine what the rate limit actually is. A rate limit should be consistently reproducible unless it's implemented in a clever way.

Would mtr[0] help diagnose this?

[0] - https://github.com/traviscross/mtr

You could test from vps in another country?

If implemented with respect to the http code, it should say 429 in the developer console.