Yes, that looks a lot like weakening from internal rust.
Inspection down the seat tube with a torch should show the extent of damage. I have a phone-mounted endoscope for this stuff.
Depending on budget and aesthetics I'd suggest the following in order of cost (low to high, maybe £50-£200ish):
1: TIG weld the cracks and get a little more life out of it, but likely to fail again.
2: TIG weld the crack then braze a 2-part split sleeve over the bottom end of the seat tube, looks like a lug.
3: TIG weld crack and braze a fillet reinforcement over the bottom end of the seat tube.
4: Lastly, remove the whole bottom section of the seat tube down to the BB shell, splice in a new tube section with a brazed internal shim, and TIG it to the BB as original.
In all cases, I would make sure that there is a good sized drainage hole into the BB shell, and treat the frame with a rust converter (such as Neutrarust), and add a waterproofing coat (Frame Saver, Waxoyl, Lanoguard etc) to the inside of the tubes where possible.
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Also worth removing paint on the chainstay and downtube areas close to the BB to inspect. All sealed frames often fail there too.
All the best,