table newindex shows invalid `need check for nil` warning if key is `false`

How are you using the lua-language-server?

NeoVim

Which OS are you using?

Windows

What is the issue affecting?

Type Checking

Expected Behaviour

t[key] = {} should throw no warning if key is not nil.

Actual Behaviour

t[key] = {} throws an invalid warning if key is false but not nil.

Reproduction steps

local CACHE = {}
CACHE[false] = {} -- ok
local key = false
CACHE[key] = {} -- should be ok as well, but throws invalid warning

Additional Notes

This happened to me in a more complex method where I ensured a key is not nil, by redefining the parameter:

function apicall(input)
    local key = input or false
    -- more stuff...
    cache[key] = {}
    return cache[key]
end

I'd like to note an annoyance when it comes to casting, the following casts all throw warnings, even if explicitly casting the variable, requiring me to invent a new variable (or forcing me disable redefining local):

---@param input string?
function apicall(input)
    -- this cast does nothing and also throws no warning
    ---@cast input +false
    -- this cast warns that it can't cast string? to string|false
    ---@cast input string|false

    -- this is what I do, it just throws an info warning, which I've disabled:
    ---@type string | false
    local input = input or false
end

Log File

No response

Start with the Lua reproduction in the issue and trace the type-checking path for table newindex operations when the key is false rather than nil. Also examine the reported cast examples, then verify that valid false-valued keys no longer produce the warning while genuinely nil keys still do.