True, whilst all surfaces in the tank are coated with some bacteria the vast majority are housed in the filter. Moving over existing gravel would help a bit, but not vital if you want to change the colour scheme at this stage. The crucial thing is the filter media.

Add new pre rinsed substrate to new tank. Fill up the new tank to about 50-60% with pre treated, warmed water (test for 24 hours first though so you know it doesn't leak) move the existing filter over to run alongside the new one, or simply add all the media to the new filter - cram it in, it doesn't have to look pretty and if it's sponge it should squidge in.

If you plan to run the filters alongside each other, the old one needs to run for about 6-8 weeks to ensure the water stays safe whilst the new media grows the bacteria colony.

Add the filters and switch on, top up the tank with as much of the ‘existing’ tank water as you can - it gets a bit mucky as you get lower so leave the last bit (fish may be happier in a bucket of existing tank water whilst you do this bit) - then add the fish, acclimatising them first in bags as you would if they were new additions.

Then, the final top up of pre treated water may be needed to complete. You can then move existing plants/add new plants, twiddle and fuss with layout as the last stage as you won't be clock watching at this point.

Hey presto, same amount of bacteria but more water volume. When upgrading like this you don't need to wait for the new bigger tank to cycle. Testing each day for a week or so is recommended so you can catch and deal with any possible small spikes that may occur in the water parameters