Where does the other end of the secondary in a solid state tesla coil connect?
It's a source of confusion, even for (some) builders of Tesla coils. Or at least, where best to connect it is.

The current that flows from the high voltage terminal of a TC has to return somehow to the bottom terminal. As the frequency is several hundred kHz, and the impedance is very high, just the few pFs of capacitance between the top terminal and 'ground' is adequate.

What's 'ground'. If you are running in the middle of a field, it's obviously the earth beneath your feet. If you are running in an apartment on the 14th floor, it's actually the mains wiring and any metallic pipes in the walls, the floor, the ceiling. Some of these may be connected together, some may be relatively isolated. This is where the spark currents may introduce voltages between (say) the line conductors and the earth conductors in your building's wiring, and upset your, and your neighbours' electronic equipment.

What people running indoors will often do is to use a 'counterpoise', a large sheet of alli foil or chicken netting laid out on the floor beneath the coil. This becomes the ground, at least the major ground at RF. Connect the secondary bottom, the mains wiring ground, and any safety gap and filter returns here.

When running indoors, it's also a really good idea to connect some X2 rated capacitors between line conductors and mains earth at the coil supply, to short these together at RF. This reduces the amount of voltage that the TC currents will induce in the wiring.