Minutes? That sounds exaggerated.
How powerful was your Atari ST compared to other machines at the time versus the machines you work with these days compared to other machines available?
Because I'm not even on a particularly new machine and from a powered off state I'm logged into Windows and starting applications within 5 seconds. And for example that's at 7680x2880 resolution, not 640x400.
POST on a Dell M640 is about three minutes. Other Dell systems are similar. POST on the workstations that I use are in the range of 1-2 minutes. This is before the OS gets control (once that happens, it's usually 15-20 seconds to a usable system).
The ST was a pretty decent performer at the time (arguably a little faster than the original Macintosh, for instance). Both the ST and the Macintosh took about the same amount of time to boot from floppy disk (though the OS was in ROM for the vast majority of STs that were built).
With that said, POST on my Z820 workstation probably takes a minute, even with option ROMs disabled, but still maybe half the time it takes an Gen8 HP MicroServer with a quarter the RAM to do the same.
On the other hand, my old IBM POWER6 server sets local records for boot (IPL) time: in "hyper" boot mode, with "minimal" testing, it still takes slightly longer than the MicroServer to turn control over to the OS, the default, "fast" boot mode takes maybe five minutes to POST, and, well, I could very nearly install Windows 10 on a fast, modern desktop PC in less time than it takes to do a full, "slow" POST.
As for simply booting such a desktop, even with all BIOS and Windows fast boot options disabled and a display connected to both internal (AMD) and external (NVIDIA) GPUs, my Kaby Lake NUC takes no more than ten seconds to boot to the Windows 10 logon screen from a fast (Samsung 970 Pro) SSD.
I also have hibernation disabled, and I've never noticed some obviously large file that might be a hibernation state on my drives (even e.g. removing a drive after a shut down so there was no restart where it could've been deleted).
https://superuser.com/questions/1096371/why-is-windows-hiber...
Still it isn't much longer for me to restart after fully shutting down (with a more recent system and SSD), just more time in Windows and less in the BIOS (and shutdown is instant with "fast startup" turned off, which is better for me since I usually pull the plug after turning it off). About 20 seconds (counting myself, not timed).
Still not as fast as DOS + Windows 3.1 IIRC, but not too bad for turning it on once or twice a day. I have also noticed the many things that have delays now in places there weren't 30 years ago, but I don't think boot times are the best example of this. I might appreciate the twitter rant if not for the completely incorrect diversion about google maps (you can drag parts of the route to make changes and get exact distance, better than paper maps and with much more details about what is nearby). IMO, computer interfaces should have a tool focus, doing basic tasks quickly and reliably so that users can learn to use it like they would a physical tool (while also not making users do extra work that could be done quickly and reliably). Now everything tries to use the network all the time, adding random delays as well as compromising privacy.