I'm not sure exactly what your "+HS" means, but from the images it looks like you're trying to implement something where the master holds off until the slave does a 1->0 transition on that pin. That's probably the key here.

You could set a global volatile uint32_t HSCNT and attachInterrupt on FALLING on that pin and simply increment the HSCNT on each fall. Very fast and it signals when the host has seen a falling 1->0 transition, governed by the hardware itself so no chance of missing things.

In the main app, store a copy of uint32_t oldHSCNT = HSCNT; before the transaction. Then after the transaction simply do a while (oldHSCNT == HSCNT) { /*noop*/ } instead of your while loop.

I've not tried it, but off the top of my head it's be like:

volatile uint32_t hscnt = 0;

void HSFall() {
  hscnt++;
}

void setup()  {
  attachInterrupt(HSPIN, HSFall, FALLING);
...
 for (int d = 0; d <= 5; d++) {
    uint32_t oldCnt = hscnt;
    SPI.beginTransaction(SPISettings(speed, MSBFIRST, SPI_MODE3));
    SPI.transfer(wr[d]);
    SPI.endTransaction();
    // Busy wait for HS 1->0 transition
    while (oldCnt == hscnt) { }
  }
....
}

You could also just ensure HSPIN is 1 before your programmatic loop like

    while (!digitalRead(HSPIN)) {} // Wait until HS goes 0->1, slave started working
    while (digitalRead(HSPIN)) {} // Wait for HS 1->0

You of course need to be sure there are no glitches (bad signal quality) on the HSPIN for either method or all bets are off.

good day!
I think I figured it out))
the reason is the "hyperactivity" of Pico Pi)). I reduced the operating frequency to 50 MHz, and the results began to stabilize. Please tell me - is it possible to further reduce the operating frequency of Pico?