When someone writes a reply asking for a source, did they actually do a short Google-search related to the claim?

no one is responsible for supporting our argument except you.

To add one more aspect: When someone writes a reply asking for a source, did they actually do a short Google-search related to the claim? It basically takes the same time to just look at the summary of the search results as asking for a source. So I assume if someone asks for verification for an easily searchable fact, then they are acting in bad faith.

This point rubs me a little wrong both on the basis that

A) onus of proof falls on the one making the claim

B) if it takes the same amount of time to find the answer as it took for them to ask you, then logically it takes the same amount of time to include a source for anyone that wants further reading as it would to make them look for it

and (most importantly)

C) you can find pretty much anything on the internet if you've got 12 minutes to dedicate to looking through all the clickbait.

The result becomes that I can say any batshit thing I want to and now it's your job to discredit your own stance for me, and if you aren't convinced, you aren't googling hard enough. Instead of just asking and finding out I got it from The Onion, which I would naturally be very against having to say out loud.

While it might not take a long time to search for something, its also not unreasonable to ask for the OPs reasoning/evidence. Outside of the blindingly obvious, if you make a claim it's on you to back it up. Even for the blindingly obvious sometimes its only clear to you. Otherwise, claims made without evidence can be dismissed without evidence.

See Russells teapot

If you notice someone acting in bad faith, don’t engage with them

I find that relentless mockery is the best way of countering a sealion. Don't cede the field to them. But also don't get drawn into a bad faith argument. Just insult and make fun of them until they leave.