How tight can I mount a TO-220 to a bus bar?

The part you are trying to get the heat out of is roughly in the centre of the black plastic part and mounted against the lead frame. Distorting the lead frame (the metal part) by overtightening will result in poor heat transfer and could even damage the bonding of the die to the lead frame or the die itself if it bends the soft metal leadframe, even slightly.

You should not overhang the part that contains the die as shown in the left part of your photo- ideally that's the part you want in intimate contact with the heat sink. The screw is offset because it's inconvenient to put a screw right through the centre of the die but you are really trying to create contact and some pressure between the part under the plastic and the heat sink. Some manufacturers use spring clips that push on the plastic itself. From an Infineon page, here is a part with a huge internal die. Keep in mind that the die is brittle silicon and the lead frame is soft and malleable.

Vishay Siliconix recommends 15 in-lb (1.7 N-m) torque for their TO-220 packages. There is limited advantage over 10 in-lb, as shown here:

It's fairly common to use torque screwdrivers and wrenches with power devices, and like anything else they may require regular calibration and testing. Inexpensive ones as used by gunsmiths etc. start at around $50 US.

Am I correct to assume that all the electronics are within the black plastic part,

yes,

and that I can therefore tighten it as hard as I would like?

No, since that would deform the metal part that you're screwing onto the bus bar, and that will not play nice with the insides of the black plastic part :)

But assuming you're not planning to use raw force:

The job of pressing the case against the metal bar is to minimize the thickness of the thermal grease layer between case and the bar. At some point, that increase in pressure will not significantly reduce the thickness any more. I'd call that "hand-fast with a common screwdriver"; but I'm sure an official standard documents that.

EDIT with the alternative datasheet that actually shows the tab is connected to the drain, your circuit makes a whole lot more sense :)

So yes, in that case, no thermal grease. Instead, I'd frankly simply solder it to the bus bar by

• applying solder paste and placing the transistors on the bus bar (not necessarily even securing them with a screw, unless the assembly could undergo substantial vibrations: in that case the screw is mandatory to lessen the risk of solder joints cracking),
• heating the bus bar from below to the point that the solder paste melts and makes a good contact,
• turn off the heating,
• and then immediately start cooling it down, probably with a stream of fresh air, to make sure the "heat wave" coming from below will not reach a much higher temperature. Don't overdo it with the cooling down, though, since rapid thermal changes aren't good for the properties of the solder joint nor the integrity of your transistor.

Note it might be easier to do this with the 263 package.

I'd suggest that if you persevere with high current connections to TO-220 packages you are creating a nightmare field service/repair scenario for yourself. For any professional application it's much better to choose a module based device such as this. Modules are by far the best when considering anything that must be bolted to a busbar assembly and they are not overly expensive today.
Once you get in the 50-100 A range then cable sizes tend to become unwieldy and have to be firmly anchored. Simple solder joints are always at risk and can become brittle over time.

For anything hobby you should consider:

1. The bolt holding down the package to the busbar for TO-220 is far too small. Even if you use the whole of the diameter of the TO-220 mounting hole size, you are unlikely to be able to achieve >10 in/lbs tab pressure with any real long term stability, even with a steel and spring washer. Pressure contacts such as this are not viable at high currents.

2. Soldering a TO-220 package is always an option but soldering multiple devices to a busbar is an unworkable solution, It's unlikely you could ever repair it.
   Solder the package to a copper strip (I use 0.125 x 0.5 x 1.25 ETP copper tabs for this purpose). These can be easily soldered in an SMT drawer (add the tab, then when up to temperature add the device with flux on the back), tabs such as these allow multiple and much larger mounting bolt sizes with reasonable torque capability. When you screw the tabs to the busbar clean the joints but do not use heatsink grease as it's not electrically conductive. Always use a steel flat and spring washer under nut and flat washer under the screw head.

3. TO-220 lead frame connections are not designed for free wire connections, especially at higher current. If you have to do this, then use a solder wire ferrule like this to ensure a stress free solder joint less likely to temperature age. You also need to support the wire, since the leadframe will break if you have even a medium vibration environment. The leadframe should not be exposed to any side or flex forces. It's a good idea to support connections like this with a two piece barrier as a stress relief.

How tight is 7nm. Use a nut and bolt w/ external star lock washer and a dab of permanent thread locker loctite will hold a to220 package securely.