Every option is a compromise.

If you're slender and wear pants that are fitted (not baggy) it's challenging. Bigger guys with loose fit pants can get a surprising amount in the naturally larger pockets.

A courier bag AKA messenger bag is the man's version of a purse, and is certainly an acceptable option. It is annoying to carry all day and keep up with. But you won't have the weird-looking pocket bulges. They come in myriad sizes and designs.

There's the "utility belt" thing where you clip a phone holster to your belt. They also make pouches for this. I think one or the other is "OK" but definitely wouldn't do both. You'll end up looking like Batman or a police officer. Things clipped to my belt are annoying to me, but some guys do it every day and it works fine for them.

Some guys wear vests with lots of pockets. A select few can actually pull this off, but, it's going to look dorky 95% of the time, IMHO.

Windbreaker or light jacket with pockets is another good option. But in the summer, not always ideal.