Pump or mushrooom valve issue?

I am now tasked with repairing a Starbuck Barista (or Saeco SIN006, same parts different colors). The owner had it for the past 20-something years, and, not knowing anything about espresso machines, had the pump replaced about 2011. I recently thought it would be a good idea to clean the somewhat clogged up portafilter, so I used the appropriate cleaner (caution: this is not a descaler) as I didn't want to use vinegar or CLR and its everlasting smell. So the good news is the portafilter and shower screen are now completely clean. The bad news is the issue I was trying to get rid of didn't go away.

First symptom

1. Whenever I close the portafilter against the running pump, the pump noise slowly dies out as pressure builds up (normal, as it is a pressurized portafilter).
2. Keeping the portafilter closed still allows some water to drip, whereas it should be fully watertight (or so I understood)

Second symptom

1. When I open the portafilter again, water should come out easily and the pump noise should increase as pressure in the boiler decreases.
2. However, this isn't the case: I only get a few drops (the content of the portafilter, basically), but the pump is still humming slowly and doesn't provide any additional pressure.

What I already tried:

• Just after reopening the portafilter, turning the pump off for a few seconds to a minute (highly variable) will usually allow a steady stream of water to come through the portafilter. By doing so, I assume I the pressure inside the boiler diminishes.
• Removed shower screen just in case = no effect, same symptoms
• Removed portafilter after pump has slowed down to a low huming noise. (WARNING: before anyone says so, yes, I know this is DANGEROUS should there be any pressure build-up in the portafilter. That's why I did so behind a wet towel to avoid any splashes. However, from symptom #2, I knew there wasn't any pressure. If unsure, don't do it) = suprisingly, no effect either!
• At this step, the only obstacle on the pressurized water path should be the mushroom valve.
• I also tried to remove the mushroom valve from the boiler, but years of lime build-up took their toll and I couldn't do it and just bent the tool. I didn't want to use WD-40 for obvious reasons.
• Dismantling the pump, just because. Here are some pictures:

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Inlet plastic tube is reasonably clean. Rust marks are actually on the outside. Plunger is a bit loose in the tube.

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Plunger O-ring isn't as tight as video tutorials on ULKA pump show it to be, but snug enough it doesn't slide off by itself.

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Plunger plastic ball appears to sit properly on the thin end of the plunger.

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High pressure side has a bit of scale build-up, but nothing out of the ordinary

What I can't try

Logic would require one to use a manometer to know the pressure provided my the pump. However, I have no such instrument.

I made a short video describing the issue. In this video, shower screen has been removed and there's obviously no coffee in the portafilter.

• 0 to 11": pump noise dies down as pressure builds up against closed portafilter.
• 18 to 27": I open the portafilter, very small amounts of water comes out, pump noise doesn't resume.
• 27" to 35": I repeat the manoeuver, to no avail.
• 36": pump is turned off, portafilter is open.
• 48": pump is turned back on, water flows through portafilter.
• 1': portafilter is closed against running pump
• 1'10": portafilter is opened again, no flow.
• 1'17": pump turned off
• 1'24": portafilter still open, pump turned back on twice, no flow.
• 1'34": portafilter open, pump turned back on after a few seconds off-time, correct flow.

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What is the problem with this machine?

Update: I ran a cycle of descaling using the recommended instructions / ingredients (100ml lactic acid in 1 l of water). I unplugged the heater element so as not to waste electricity. Water came out milk-ish white. I am now in the rinse cycle.

However, a two new issues appeared:

1. when I close the portafilter, the pump never stops. It doesn't even slow down, and water is leaking from the top of the portafilter.
2. The portafilter itself developped rust under the basket for some unknown reason

I can't even check that the original problem disappeared!

ideas?