As each Lot in your Plan has at least one carspace, other than for reasons of being too lazy to walk from there to the buiilding’s entry, there’s no reason why all residents with bicycles couldn’t use their carspace for the storage of those.
I would certainly put a stop to the practice of residents storing their bicycles under the stairwell, because as you said, it looks messy, it’s damaging the Common Property, and all that will certainly get worse unless your Plan’s Executive Committee puts a stop to it; with a barrier if necessary.
The only issue is the security of those bicycles that are stored in carspaces, particularly as you advise there’s no no garden or outdoor Common Property available for a communal bike storage.
So if that’s the case, your Owners Corporation could facilitate residents’ bicycle use and the proper storage of those by resolving to select a style of single bike security rack that suits the layout of the carspaces, making that the “standard” for the Plan, and then offering to supply and install that rack in the carspaces of bicycle-riding residents, as an alternative to them storing their bicycles under the stairwell or elsewhere.
In that way your O/C maintains some control over the style and standard of bike-racks, and how/where they’re installed within Proprietors’ carspaces; and that’s not a bad thing!
Even though a decent single-bike rack could be supplied and installed for under $100, there are 140 Lots in your Plan, so the O/C would need to plan on a defined number of installations per year.
You could seek a contribution from interested Proprietors or Tenants, but the former is paying anyway via their levies and the latter would probably want a refund at the end of their tenancy; too messy!