Give other entities access to only deposit funds in my account

The situation is actually worse than you think. The default position of North American banks is that if anyone who has your bank account details, and is a reasonably reputable financial institution, asks for money from your account then your bank will give it to them. There is literally nothing you can do to prevent this. The only way to prevent such unauthorized access is to change the account details. There are dispute procedures that may allow you to get your money back, but they are time-consuming and dependent to some extent on the goodwill of both financial institutions.

It's worth noting that most banks outside North America want to see the document that authorized the withdrawal before they let funds out.

I never provide the log in details of an account to another financial entity. I agree with you, no thanks.

My experience in the US over 20 years (finite sample of 15 or so banks) is that when you do the two trial deposits routine, it only enables the sender of the deposits to have an active transfer link. To have it go both ways, it has to be done on both sides.

I would not be concerned about setting these up between two US banks that have routing numbers, FDIC insurance, etc. That makes them legitimate.

Though I have no experience with them, I would never do this with a foreign entity nor anything like Bitcoin or other. Subsidiaries of foreign banks meeting US regulatory standards (chartered in the US and members of the Federal Reserve) would be fine (Barclays Bank, Deutsche Bank, etc.).

This type of service does exist, although it is usually something attached to business banking accounts, not personal accounts. You are actually issued a second account number that is linked to your account but is deposit-only. You would just need to ask around at banks to see if anything like this is available for your personal account.