First, with the rear wheel held off the ground, or the bike upside down turn the pedal by hand while inspecting the chain and rear derailleur. Likely issues:
- The chain tries to shift to another cog and fails. Gears need adjusting.
- The derailleur jumps as a stiff chain link passes through it, possibly with the chain jumping on the sprockets as well. Can possibly be freed up, or replace the chain.
This won't catch everything. If the chain and/or teeth on the sprockets are really worn, the chain can jump under load but not in an unloaded test. This is likely to mean a new chain and cassette. You can check for chain wear by measuring with a ruler.
All these forms of slipping can cause a clunk and, especially if you're pushing hard, a significant wobble.
Road testing includes trying in all your gears. Slippage caused by worn parts is more likely in a small sprocket, and small sprockets wear faster than bigger ones. You've pictured it in a small sprocket and the middle chainring. If you routinely start out in this gear it could be very worn as it will take a lot of torque over few teeth. Of course it might just happen to be in that gear from your testing.
Your latest comment - inability to accelerate - suggests an issue I've struggled with, and that's freehub issues (though it's a silent fault IME). To check, do the pedals spin freely at this point, jump unpredictably when pushed, or what?
Chains age from distance rather than time, but if you haven't ridden enough in 3 years to need a new chain, it's possibly got stiff in places. Sometimes stiff links can loosen a bit for one ride, then stiffen up again.