pyomo: an indexed variable should be linear or integer depending on the variable index

There are a couple ways you can accomplish this. For the following, I am assuming that your params.Installable_units = ["GasPowerplant", "batterystorage"]:

If the number of elements in new_units_built_set is small, then you can use a dictionary:

model.new_units_built_set = pyo.Set(initialize=list(params.Installable_units))
model.New_UnitsBuilt = pyo.Var(model.new_units_built_set, 
    domain={"GasPowerplant": pyo.NonNegativeIntegers, "batterystorage": pyo.NonNegativeReals})

Or if there are a lot – or there is a simple formula to get the return value – you can use a function (rule):

model.new_units_built_set = pyo.Set(initialize=list(params.Installable_units))
def _new_unitsbuilt_domain(m, p):
    return pyo.NonNegativeIntegers if p=="GasPowerplant" else pyo.NonNegativeReals
model.New_UnitsBuilt = pyo.Var(model.new_units_built_set, domain=_new_unitsbuilt_domain)

Or you can just set everything to one value and override later (assuming you are using a ConcreteModel):

model.new_units_built_set = pyo.Set(initialize=list(params.Installable_units))
model.New_UnitsBuilt = pyo.Var(model.new_units_built_set, domain=pyo.NonNegativeReals)
model.New_UnitsBuilt["GasPowerplant"].domain = pyo.NonNegativeIntegers

All of these will produce:

>>> model.pprint()
1 Set Declarations
    new_units_built_set : Size=1, Index=None, Ordered=Insertion
        Key  : Dimen : Domain : Size : Members
        None :     1 :    Any :    2 : {'GasPowerplant', 'batterystorage'}

1 Var Declarations
    New_UnitsBuilt : Size=2, Index=new_units_built_set
        Key            : Lower : Value : Upper : Fixed : Stale : Domain
         GasPowerplant :     0 :  None :  None : False :  True : NonNegativeIntegers
        batterystorage :     0 :  None :  None : False :  True :    NonNegativeReals

2 Declarations: new_units_built_set New_UnitsBuilt