I take steps to prevent my traffic being monitored like using Tor whenever I make a suicide-related searches. I avoid privacy-invasive services as much as I can so I don't have an facebook, twitter or google account for example and try to use free and open-source software as much as possible like firefox, linux, tor, searxng etc.
I highly doubt anyone would get into trouble for looking anything up. The only way you realistically could get into trouble would be if you said you were going to do it while using a privacy-invasive service such as a Google service. Google has been known to automatically notify the police about suspected child predators and realistically could just use decide one day to also do that with suicidal people.
That's why I use a VPN.
It's not impossible for someone to track you when using a VPN, but it makes it much, much harder
VPNs are not a solution to internet privacy issues, you have things like browser fingerprints, unique identifiers and more. You also have the problem of VPNs being compromised or just selling your data. Using the Tor browser would be a much better alternative for web browsing in my opinion.
TOR plus a VPN that is not within Five Eyes or Nine Eyes and doesn't keep any logs. Fourteen Eyes VPNs are there as well but they're better than nothing.
The government can track your internet usage through download and upload speeds via TOR and can figure out relatively what you've been doing on it. Maybe not exact web pages, but they can know what you upload or download.
Generally speaking, we don't recommend using a VPN with Tor unless you're an advanced user who knows how to configure both in a way that doesn't compromise your privacy.
You can find more detailed information about Tor + VPN at our wiki.
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In my opinion I don't see much reason to use Tor + VPN for just sasu. I'd only consider it if you were doing something very illegal. I don't see the point for anyone to put enough resources to de-anonymize your Tor usage just for wanting to CTB. Most people get caught from saying too much or making other OPSEC mistakes unrelated to Tor.