I think people are confusing pen and paper RPG immersion with video game design. There's quite a bit of suspensions of disbelief we've got to work with when we're talking about video games. Very few people are ever going to complain about being able to carry your entire inventory with you in Dark Souls, because functionally an inventory limit would only serve to make you backtrack to a bonfire and redo a section you aren't struggling with. Dark Souls manages to be an incredibly atmospheric game despite what may look like a glaring flaw in its depiction of reality, and in fact would become less atmospheric if you did have to micromanage your inventory because an inordinate amount of play time would be spent in menus rather than playing the game.
And it does this while still having an encumbrance system! Dark Souls has two inventory systems, the one that's your bag of holding that just carries all your loot and junk and that doubles a repository of cryptic contextual lore and the one that depicts what's actually being carried on your person for use in combat. Heavy armor makes you move slowly, using backup weapons also weighs you down.
Meanwhile, in a tabletop RPG we do something that's pretty much the same. What GM in the history of mankind has ever actually tracked encumbrance in anything? Precisely two, an angry old man and the poor kid he's raised in his basement, isolated form the rest of society, to do the same. Every GM just abstracts it away by saying you've got your stuff stashed in a cart or a car or a hideout and if the party wants to swap stuff around the GM just says "OK, you do that, now you're back so what do you do now?" Still not wasting any precious time on depicting something that the game isn't about.
Backpacks aren't thematically appropriate for the setting, this isn't a wilderness survival where characters are expected to carry everything they own on their literal backs. Everyone should have at least enough property to hold their stuff, whether that be a rented storage unit, a safehouse, a car, a shopping cart, what the hell ever. But it is super thematic to worry about concealment of what's being carried. Pistols suck compared to automatic longarms, but the former are more closely associated with cyberpunk because it's something that can be hidden.
So why not just take a page from Dark Souls and go with what RLKing1969 suggests? Unlimited storage abstracted away as being kept at another location guarded by someone that knows better than to peek under the tarp, but anything you can use that has to be on your person has a Conspicuous rating. Things like holdout pistols have a really low rating, and embedded cybernetic weapons like spurs have a rating of 0 as they hide in your limbs. Anything that draws attention has a higher rating, and your overall Concealment rating is determined by the most conspicuous piece of gear you've got equipped. Having both a holdout pistol and an assault rifle is a bit counterproductive as everyone's going to see that big 'ole assault rifle, so when you're not going in guns blazing it's important to have weapons that match the situation.
Some gear might allow you to conceal other weapons, trenchcoats might replace the relatively high Conspicuous rating of weapons that fit in them with the reasonably low Conspicuous rating of the trenchcoat. Said trenchcoat itself would have a higher Conspicuous rating than if you were wearing regular street clothes, but for walking down in the gutters of the city it's just fine. Big weapons like rocket launchers might fit in cases that themselves are pretty Conspicuous, but that's still better than having the weapon just slung over your shoulder. You still have to spend precious seconds taking them out of their case before using them, though, a trade off that makes them useless compared to just taking an SMG tucked away in your coat unless you know that your'e going to be needing that rocket launcher for an extended action sequence.
It avoids the pitfalls of having super fiddly inventory management while still giving you a reason to not run around like a super soldier all the time. Anything that has a Conspicuous rating has to be picked up first at a checkpoint or safe house or whatever, but everything else is just in your general inventory. You can choose to carry Conspicuous items you find or buy and accept any new rating you get from it, or you can have it sent to your storage for free (so something like walking past a security checkpoint unarmed and then buying a gun after the checkpoint or beating someone up to steal theirs is a valid strategy). It's not "realistic" but neither's much of the setting, the important bit is that you're behaving more like you have something to hide, like you're a lowlife avoiding the law.