tl;dr:
Scammers pressure you with time limits for actions. Such as "our team will lose if you don't sign up for our tournament in five minutes :(((" or "I will ban you if you don't quickly send your items to be checked"
You CAN'T lose your account if you have done nothing. Nobody will EVER invite you to a tournament randomly. You aren't getting banned from anywhere if you haven't done anything. False reports don't exist. Remove them from friends and move along.

Here is Valve themselves tweeting about scams: https://twitter.com/CSGO/status/1503452506961063936
It reads:
"A reminder that no one from Valve will ever contact you through Steam (or Discord, or anywhere) and threaten your account or request items. If someone claims to work at Valve and they are threatening your account or items you should report and block them. This is always a scam."

This same can be applied to any site you have or have not come into contact with. There are no verifying or checking processes for items that include items leaving your inventory. Sites are not interested in banning you for random reasons and if they are, they will NOT contact you about it.

Googling site names as "backpack tf" with a space in between will show you common results and experiences from others on other sites. Do this process with any strange site you come across or are told to go on.

Newest tournament scam is done with bots. They will try to get you to a "SPRING CUP" or whatever season it is. YOUTUBE VIDEOS ARE USED. Large prize pools. There are no large prize pools for TF2. If you are unsure if it's a bot, ask them a question and if it's not answered, then it's a bot. These will attempt to hijack your account with fake login pages, like many other scams.

Here is a guy pretending to be a Valve helper. https://imgur.com/a/tfPYZbP
There are people saying they're a "Valve helper" or a community moderator for Valve. These sort of people WILL NOT contact you through Steam chat. They will tell you that you have "duplicated items", "items with with an incorrect index pattern" or some nonsense like that, telling you that you will be banned if you do not take action. These are completely fabricated lies.
They then want you to visit some non-Valve website or trade your items to a "bot" (their friend or them on another account) that will "check your items" so you won't be banned. Nothing will happen when you remove them from your friends list.

Some simpler scams exist as well. Guy adds you, tells you "I want to promote this website, I will pay you" or "We have a sixes game starting in this tournament in 30 minutes, we need a player". These websites are often named tf2(random word) .com or something similar. Situations like this do NOT exist. No one wants some random guy (you) to play in their team or promote their site. There are better ways of marketing and gettings mercs in TF2, adding a random guy is not that. Do not type your login info to sites you cannot trust. Check again with the site googling to see if someone on Reddit or somewhere has experiences.

These scammers make you hurry through these things to pressure you into doing things. This is only to stop you from thinking correctly. If you are sitting pretty with your inventory and account, nothing can happen to it. Nobody messaging you through Steam chat (or Discord?) can ban you.