hey, just want you to know you're not alone. i am about ten years younger and should be wearing diapers every night (sometimes i skip it and dehydrate myself or don't get any sleep from peeing so much). i guess i don't need diapers all day long yet, but i have worn both pullups and taped diapers to work at times. let's see... you could take off pull-ups easily while keeping pants on by ripping them at the side seams, but pulling a new pair on without taking off the pants is impossible. for out of the house wearing, the tape variety are honestly so much easier as others have said. maybe you might be able to find some thinner-profile taped diapers for daytime. I like the tykables daily little builders diapers, and i have had some success with northshore's supreme lite. if you strongly prefer pull-ups, the northshore gosupreme pullups are the only pullups i'd ever want to buy again since they have actual capacity to hold a full wetting, and they come with a little sticky tab to discreetly roll up for disposal--for sure recommend them over others. (i am sure you can tell by my use of the word 'diapers' that i'm not from the uk, but i hope my experience can still help).
larger pants and long shirts are great to use to cover up any bulk. i sized up all my clothes. i have used the gary wear diaper covers before, they are helpful but i don't always find them too comfortable (by necessity, the leg holes are very tight on them).
i am often too embarrassed to change in public settings, but i have done at work and been okay. the bathroom is just right next to the break room and you can hear everything. i mainly use my car as a "safe place" to change, like in the back seat with an absorbent pad under me.
i guess it would not be very socially acceptable for me to carry an actual purse, even though i'm non-binary i look fully male. so anyway, i'll typically bring a bag that looks like a laptop bag with a shoulder strap and can convert into a backpack. they look professional enough for work and could be toned down for casual use. they are large enough to carry up to 4 high capacity diapers, baby powder, and wipes. plus i attach a little hand sanitizer keychain thing to the strap, which i think is helpful to think about. you might like to carry something like this, but also some of the big purses i see women carry i guess could hold two diapers easily. i think it's good to have this as a separate bag to your main bag, or to stash the diapers in the 'laptop' part which is somewhat closed. just in case someone sees inside.
lastly, i would recommend you to check out the diaper dynamo's videos on youtube or tiktok, he has many daily use tips and his videos are just aimed at destigmatizing diaper wearing for younger adults and anyone that needs or wants them. he also has some kind of diaper cover shorts that i can't remember the name of, they looked comfortable and you might want to check those out.