You said " Without a dehumidifier my tools get condensation on, which in turn slowly rusts them - any paperwork left in their doesn't stay flat, and brake discs/nuts/bolts will slowly rust also.

Dehumidified everything in their stays perfect, which for a few pence of running costs after initial outlay is worth it imo. It also doesn't smell of damp, which is far more pleasant, and I can hang art work without fear of it being spoiled.
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That would ring alarm bells for me unless the house and garage were old. Our houses bar one have all been modern because thats what SWMBO likes. Never had an issue of tools or fasteners going rusty or a damp smell, and I have a silly collection of tools. No de-humidifier. Might be worth checking the damp proofing.

You cant lose by having a de-humidifier though it does cost to run and does require a good door seal. But it shouldnt be necessary in a modern build any more than it is necessary inside the house where the people and processes like cooking give off lots of water vapour. OK tyhe inside is heated but that only allows the air to hold even more water vapour.