improper inference of lambdas and dataclass constructors used as generic decorator arguments

Bug Report

I'm attempting to make some registry-like decorators to be generic in my code and bumped into mypy complaining about my constructs.

The point is: concrete decorators should be defined with [HandlerT: Handler] type variable. It's to correctly decorate functions with non-exact (but matching) call signatures. Signatures should be preserved.
The rest registry functionality to be handled with broadly generic _decorate function.

I supposed decorate1, decorate2 and decorate3 should behave the same. Among them, lambda version preferred due to its conciseness and flexibility. Nevertheless, only decorate3 passes mypy checks. FTR, pyright passes them all.

To Reproduce

from collections.abc import Callable
from dataclasses import dataclass

type Handler = Callable[[int], str]

@dataclass
class Wrapper:
    handler: Handler

registry: dict[str, Wrapper] = {}

def _decorate[WrappedT](
        key: str, wrapper: Callable[[WrappedT], Wrapper]) -> Callable[[WrappedT], WrappedT]:
    def _wrap(handler: WrappedT) -> WrappedT:
        registry[key] = wrapper(handler)
        return handler
    return _wrap

def decorate1[HandlerT: Handler](key: str) -> Callable[[HandlerT], HandlerT]:
    return _decorate(key, Wrapper)   # line 27

def decorate2[HandlerT: Handler](key: str) -> Callable[[HandlerT], HandlerT]:
    return _decorate(key, lambda handler: Wrapper(handler))   # line 31

def decorate3[HandlerT: Handler](key: str) -> Callable[[HandlerT], HandlerT]:
    def _wrapper(handler: HandlerT) -> Wrapper:
        return Wrapper(handler)
    return _decorate(key, _wrapper)

@decorate1("add1")
@decorate2("add2")
@decorate3("add3")
def add_handler(x: int, y: int = 0) -> str:
    return str(x + y)

@decorate1("inc1")
@decorate2("inc2")
@decorate3("inc3")
def inc_handler(x: int) -> str:
    return add_handler(x, 1)

Expected Behavior

all of decorate1, decorate2 and decorate3 forms are correct, no errors shown

Actual Behavior

wrappers.py:27: error: Incompatible return value type (got "Callable[[Callable[[int], str]], Callable[[int], str]]", expected "Callable[[HandlerT], HandlerT]")  [return-value]
wrappers.py:31: error: Argument 1 to "Wrapper" has incompatible type "WrappedT"; expected "Callable[[int], str]"  [arg-type]

Your Environment

• Mypy version used: 1.19.1
• Mypy command-line flags: -
• Mypy configuration options from mypy.ini (and other config files): -
• Python version used: 3.12

Start by placing the reported reproduction in wrappers.py and running mypy 1.19.1 with the shown Python 3.12 code. Compare the diagnostics for decorate1, decorate2, and decorate3, then trace generic callable inference for the dataclass constructor and lambda. Done means all three decorator forms type-check without errors while preserving the reported signatures.