Missing the 3.2 or 3.3V rail would make the deck pretty quiet with no power to the audio IC's. QU01 is the 3.3V reg, beta >200 not sure how much current it supplies, highest during record. If it runs hot then there's a short -circuit downstream. Your curve tracer might not be dependable if it says it's open but it's not? The part might be fine.
NTE253 is big TO-92 tall compared to the 2SD1020. I like Zetex E-line parts like ZTX690B BUT they have different pinout EBC ve ECB and hard to get in the semi shortage. You could try the NTE253 to see if it makes a difference temporarily. CU01 1,000uF 6V might have shorted, you can measure the voltage drop across RU01 100R.
JK02 pin 9 goes low when the Pause button is pressed, which turns on mute switch QU02. QU02 collector high at 14V means it's on and muting in Pause mode.
JK02 pin 8 goes low when the Stop button/Auto Stop is pressed, which turns on mute switch QU03. QU03 collector high at 10V means it's sorta on and muting in Stop mode. CU02 leaky, RU03 I think you replaced, and otherwise it's a bit of work to troubleshoot this.
So I'd leave the muting stuff for later, first get the 3.3V rail up and working.
Smokey thanks for the scan. These PMD430 tape decks were out for at least 10 years, pretty impressive for a portable model.