Keep in mind that single-tapping isn't a bad habit. I can't remember if it's Lifeline or someone else, but you can reach the highest echelons of play only using one button. However, it is generally recommended you don't because it doesn't put as much stress on one single finger and it's just generally easier to play with two.
if you do want to try to move away from singletapping, Furry Hater has the right idea. Start playing maps at least somewhat below your usual comfort (I'd say probably mid-high 1* to low 2* NM at a guess) and practice switching after every color change. As you get more used to that, then you can start switching during a single color sequence--say, 1 and 2 are z, then 3 and 4 are x. Last in this step is to start switching every number as if you were playing a stream in slo-mo.
IMO it's highly important that you stay at that SR range this entire time. You want the low SR because the focus is on getting the muscle memory right to do the alternating (to whatever degree you want) without conscious thought. Adding in extra difficult through mods or tougher maps at this point will hinder that ability because now you're focusing on more than just what you're doing with your hands. Mods should never be used at all until you get back up to your original comfort zone, IMO. As for difficulty, once you feel you have the muscle memory down pat, start working your way back up while keeping that playstyle in mind. I'd argue you can go slightly higher as far as SR jumps (.4-.5* instead of .2-.3*), but no more than .5*. This not only allows for a better curve toward playing the way you want, but also allows you to actively spot where you might need to make adjustments based on parts where you're struggling (i.e. difficulty alternating between certain pattern changes, dips in coordination on certain patterns, fingerlock, etc.) before you encounter them on more difficult maps.
This WILL take you months at minimum to get used to, if not longer. I personally developed what I consider a semi-hybrid style because I primarily only alternate between sliders (it helps me ensure I'm not dropping slider-ends), and I'd argue it took me at least a month or two to feel comfortable with it even though it was relatively early on in my actual rise in playing Osu (like, probably back in April-May of 2021--don't let my join date of 2016 fool you, I barely played then and then dropped the game entirely until I came back in 2021 if you look at my playcount graph).
I still cannot stress enough how important it is that you spend a good amount of time in lower difficulties committing this to muscle memory before you even touch a map even .5 or 1* below your "usual", though.