I bought a toilet tank for replacement purposes. The shut off valve is not shutting off the
Entire water flow to my tank. I can see & hear hear water entering the tank. I tried hand tightening the shut off valve but dare to go further for fear of damaging the connection. I am afraid if I disconnect the supply line my bathroom floor will be flooded.

If the stop cock under the tank is not closing all the way you will need to shut down your main and open a fuacet to blow off pressure. Your shut off valve may be a 1/4 turn variety or it may take several turns. They are not hard to replace or expensive, about $6. Can't be more specific since I don't know if the stop is threaded onto a supply line or soldered but in any case you should replace the stop cock. If it is threaded be sure to apply 3 full wraps of white teflon tape to the pipe thread, if soldered remember to disassemble the valve and remove the stem before soldering.

You can add a retrofit 1/4 turn valve on top of the valve that you have. It can avoid unpleasantries of replacing the permanent one. Some are extremely difficult.

KISS are you thinking of something like a stop cock that is compression on both ends? That would work and the dribble on the floor during the install won't be too bad. It sure will look like hell but who looks at angle stop cocks anyway.

Nope. I'm thinking of one of these things. It's a whole lot easier to turn the toilet off with a 1/4 turn than to turn, turn, turn etc. especially when there is a problem. It's well worth it.

The angle stop is soldered and a real pain to replace.

Any idea what to do with the rusty eustacheon.

Yep, cut it off with aviation tin snips and then buy one that is two pieces with a hinge that allows you to wrap around the pipe. I have seen some plastic one with a chrome finish that have a split and can be wrapped. Your pic is pretty much what I pictured just not compression on both ends. Nice tile, when are we going to rip it out? Just Kidding.
Bob