I would definitely change his cage if the current cage is less than 80cm x 50cm (width and depth)
. But definitely wouldn’t change it for the Pico cage. The floor area is too small snd it’s too tall so there are fall risks (despite the shelves). Also the house is right at the top, too small and has a solid base. Hamsters are ground dwellers who like to dig and forage for food.
A good upgrade would be the Hamster Heaven or Hamster Sky (both the same cage - different contents). Both are 80 x 50 but not too tall and will fit a 28cm Syrian wheel. Or the Savic plaza from pets at home. That is 100cm x 50 cm but more expensive.
The hamster heaven and sky do come with tubes but honestly it’s better to remove them and give them tunnels at floor level instead. With an 80 x 50 or bigger cage they have more floor area so can have normal behaviours like digging, foraging etc and have their house snd toile all at ground level. Because they really need a large ish house that is open underneath snd sat directly on the substrate. It’s more hygienic and allows them normal behaviours like burying hoards under the nest. They will also use a potty tray if the house is at ground level.
None of those cages comes with a decent house so you need to add one. Toys snd houses don’t have to cost a lot though - a shoebox makes a good house (cut the base out snd use the lid as a lift off roof to check inside). Pringles tubes make good floor tunnels.
A good set up would be the hamster heaven with the top penthouse removed, the tubes removed, just one shelf left in - the solid one, a house added and a 28cm truxie wheel- that will take up most of the space but still room for the odd floor tunnel and toy etc. The cage does come with a roof hanging Sputnik which is ok.
Honestly your hanster would be happy as Larry with a set up like that and won’t miss the tubes - the tubes tend to encourage abnormal behaviours like nesting and peeing in them snd blocking them up.
There is a real shortage of hamster cages right now or I’d recommend a few more. But think - more floor area, less height.
Moving cages can be very stressful for them but not if it’s done right. I let them play in the new cage the day before moving - with some substrate and any news items in it. Then the next day out the hamster somewhere secure while you move everything across (eg in a pet carrier in another room so they don’t get stressed hearing and smelling you messing with their cage!
When moving things over don’t clean anything - resist! Move all the old substrate across on top of any substrate already in the new cage. Move any other items you’re keeping from the old cage. Try and set it up do everything is in a similar layout even if it’s a different house and wheel - eg wheel back left, house centre right under a shelf or whatever. Carefully save the nest and hoard and move those over inside any house. You could prune the hoard a bit if it’s very large or peed on but try and save some of it.
With this method the hamster should settle very quickly. They can still be nervy snd skitty for a few days but nothing like as much as a cold Turkey move. It’ll then take about 10 days to two weeks before they’ve fully adjusted to the change and after that you’ll see a happy confident hamster enjoying the space in the cage and loving the bigger wheel