FWIW, I had the authorized Mazda shop diagnosed my car. Even though the steering lock was working properly on my appointment day, the diagnostic computer found the error code (96, for DTC B1026 - status 8A) stored in the memory. Also, using the testing procedure (locking/unlocking many times) it was able to re-create the 96 code. Unfortunately, the only solution the shop offered was replacing the entire START STOP UNIT - for a price I’m not in position to pay right now 
Also, they replaced the secondary immobilizer battery which solved my “warning beeps” problem (even though I had installed what was supposed to be a fresh battery just several months ago). All in all - even though the issue being mentioned in this thread’s header has been resolved - the amount of cash I left there for diagnosing - but not solving - the much more serious problem is rather frustrating…
Thanks to everyone, nonetheless
Piotr