I haven't tried it myself, but I believe if you bring the original proof of purchase or invoice with you to the Apple Store to prove you/your institution owns the machine then they may be able to do the reset. A call to AppleCare never hurts either, they may be able to clarify or save you a trip.

Short version is that you'll need to take into the Genius Bar or an Apple Authorized Service Provider with Proof of Purchase

https://support.apple.com/en-us/HT204756

Long version is, the last time I had to facilitate this, it was a drawn out process, after verifying ownership, involved a long UUID string, and then sending in an escalation to get an equally long hash back, to unlock the device.

Go to the Apple Store with and make sure you have the following:
Proof of Purchase
Identification
Letter with company letterhead stating that you are an employee and are authorized to get the computer unlocked

They should be able to do it same day (if not right there and then) depending on how busy that Apple Store is.

Can anyone advice if above solution still applies for newest laptops?

We've locked the computer with Jamf Pro and unmanaged it without backing up the lock code. After few weeks all the completed commands disappeared :(

Is there anything that can be done?

It's the same process, unfortunately, but it looks like they have that available to setup online now: Activation Lock - Support (apple.com)