Even if he manages to find it, would it still be considered
his
property?

As far as I know, in most countries, whatever lands in the trash becomes property of the city/government. So even if he finds it, the
governmetngovernment could easily sue him and take it back? That would suck but for almost a billion USD, I imagine that would happen.
And what happens if someone else finds it first? Is it still considered his property, legally? He threw it away so he relinquished the ownership rights?
Has he tried to find the lost private key to the 8000 bitcoins at
https://bitinfocharts.com/bitcoin/address/198aMn6ZYAczwrE5NvNTUMyJ5qkfy4g3Hi in some other way ? As I understand the privat key he lost looks like this
5Kb8kLf9zgWQnogidDA76MzPL6TsZZY36hWXMssSzNydYXYB9KF but only the first digit "
5" is correct, and the next digit is
K, H or J5K0000000000000000000000000000000000000000000000000
5H0000000000000000000000000000000000000000000000000
5J0000000000000000000000000000000000000000000000000
Nope, not even our most advanced super computer could brute force it, even if it had a million years time. No chance.