Even the most mundane trip can turn into an adventure if you're not properly prepared. A change in weather, multiple punctures or some unlikely mechanical problem, a medical issue. Just overcoming problems so you can get to where you intended to go can give a lot of satisfaction as well as increasing your confidence in yourself and your bike. You could throw loads of money at a specialist bike or ride a budget clunker that you've modified to suit yourself. In the end it boils down to just you and the bike, and what you do with it.
When I started out my inspiration came from "Journey through Britain" by John Hillaby (a walking book but very much a journey of the mind), "Adventure Cycling in Britain" by Tim Hughes and similar publications. I didn't become a club cyclist or join the CTC until much later. I was just an isolated bearded weirdo on a bike until I realised that there were indeed other non sporty cyclists like myself and there was a body of knowledge that I could access. That was a time of pushing the boundaries and finding what I could do, on road and sometimes off road. Definitely Colin Mortlock's stages 3 to 4 at that time.
Over the years, despite enjoying being out on a bike, things became a bit humdrum and life sort of became an obstruction to longer trips. A lot of stage 2.
More recently with retirement I began to cycle more but during lockdown I discovered recumbent bikes and every ride, no matter how short, became an adventure of self discovery again. Riding a recumbent bike has revitalised my cycling life and I've cycled further recently in a day than I have for decades. Initially stage 4 (at least in perception - from "Oh God! I'm gonna die!" to "Whee!! This is great!" and sometimes back again.) but settling down to more stage 3 as my skills and knowledge improved.
Although I like to plan stuff on line, generally I use paper maps on the road. Each to their own. I generally cycle alone, so am pretty self sufficient.
The main thing about whether something is an adventure or not is whether you yourself think it is. Other people (especially non cyclists) are amazed that you rode "How far? Where? You must be bonkers!" on a bike. Maybe some forum members might scoff at others' achievements too-"Ha! Call that an adventure? I could do that in my tea break!". There is no definitive answer. It's purely subjective.
As
@chriswoody suggests, it's a state of mind as much as anything else.