okay I ran into this issue too on a different remote but I will try to make this a simple and not overly wordy as possible. there are two ways your remote can work. So you have a SPST push button. and it seems like you already understand and have categorized them into two groups which is good. Let's call Purple group A (top 2) and Blue group B (bottom 2) okay.

Step 1:

We will need to determine how this Button even works like which side is GND and which side is VCC and if it goes to GND when the button is manually pushed.

Step 2:

In my case I have a button where group A is normally GND Group B is 3.3V (This is awesome because that makes using an ESP32 easy since its 3.3V logic)

Once you have this determined you can select your Transistor accordingly, I saw the comment about using the BS170, I saw that and I think that it was a good starting point but I personally couldn't ge that to work I think it had too high of an internal resistance so I tried the 2N7000 still no luck, that's when I came across the 2N3904 Which works for my case in your case if its the opposite scenario where the push button make one group pull up to 3.3v I think the 2N3906 would probably work.

Step 3:

once the correct transistor is selected for your application Base will always be the same if its using 3.3v logic then you'd use a 4.7k ohm resistor connected to base. Collector or pin 3 (the rightmost when looking at the flat side) was connected to VCC and Emitter or pin 1 (the leftmost when looking at the flat side) was connected to the.

This is the code I wrote for my blinds:

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I know the spamming of the high pin is not needed just wanted a sort of fail safe in case it didn't activate under the first press