I don't even know how you're supposed to trade without a premium stash tab.
By buying stuff from other people. If you really need to sell something worthwhile, use trade chat, TFT and other means if somehow by finishing your first league or a few of them you still haven't dropped like five bucks.
To find an item you're looking for you have to go to a third party site
It's an official first party website on the pathofexile.com domain with an API that works directly with the game, you don't know what you're talking about.
copy and paste the 'buy text' into the game's chat
No, you just literally click the button that says SEND TRADE next to the item you want, and that's it.
the seller must manually find the item the buyer is looking for
It's directly highlighted in your stash for convenience and even tells you exactly where it is, you don't need to "find" anything.
even though the item and price were determined beforehand, scamming can still happen. So apparently you can set a price for an item in the stash and a third party site can track it, but your own fucking client cannot?
You have to mouse over and examine each item that you're sending and receiving just to prevent scams. If you traded even once in the game, you'd know this. Also the ones where the correct item isn't locked in automatically is because the offer says ASKING price, which means you can work something out in the process if you want.
For the same instance you just press one button to teleport to the guy's hideout and that's it. It's more hands-on with directly interacting with players instead of it being an auction listing, and I personally don't see a problem with that. If the dev wants people to directly trade with each other instead of having a one-click FFXIV auction that's their decision. The website's already there to make your life easier with this instead of shouting on trade chat all day. I never had a problem or an inconvenience with buying or selling regardless of builds and farming strats, even if you're selling like 500 maps in bulk just make an offer on TFT which takes a minute and someone will hit you up. All in all, try playing the game. Going all in to play SSF, which is a very specific experience, just because you can't bother to find a minute to buy an item that you want sounds like a miserable experience, and I doubt you got very far. People usually play SSF because they like the in-depth crafting system and having the experience of making it completely from drops, it's a league of its own with unique gameplay, but if it's just from trading system butthurt, that's called clownmode. Basically the "look ma, no hands!" moment.
The reason why I don't mind it being direct interaction with players is because I've met many people during trade that I just made friends with, who helped me out, and we played the game together and did bosses and map runs together and are in contact during leagues. It's very useful for example for crafting shit that you don't have for your items by giving it to the dudes in the guild who have it. So yes, the whole direct-interaction thing does in fact work for getting involved in the game community.