When I first started with Premium, you could toggle shuffle mode on or off before hitting the play button. But then that went away and there was basically only a Shuffle button, so you had to do the sequence like here (from 2022)

https://www.drmare.com/spotify-music/play-spotify-album-in-order.html

but at first you didn't have to do this bit

Step 4. Open the "Now Playing" page and turn off the "Shuffle" button.

And I think at that time the forums were saying it was only the Android app where you had to do this (and I want to say that desktop/web app were indeed not putting me through these shenanigans at that time, was a probably 4-5 years ago, maybe more). And then when I further had to start doing that 4th step of disabling shuffle in the now playing screen I had just had enough and cancelled.

Other posts from 2023 seem to indicate this is now the standard UX on all platforms

https://www.audkit.com/spotify-music/spotify-play-album-in-order.html
https://integraudio.com/play-songs-order-without-premium/

edit:

Here's a community thread going back to 2015 ("modo aleatorio" means "random mode") with commenters chiming in through late 2022.

https://community.spotify.com/t5/Android/Playing-albums-in-order/m-p/1262705

So I guess I may have my timelines a bit off, but I strongly remember the Play button originally having a little sub-button overlay you could tab to enable or disable shuffle before hitting the Play button proper.