If your employer refuses to disclose # of issued shares, you have absolutely no way of valuing your shares. I can't think of one good reason why they'd be unwilling to give you this information, and as a result, I'd actually advise that you value your shares to be worthless.
I had that once and I told the hiring manager that without that number I have to treat them as zero value. He said that was reasonable, and we negotiated on salary instead.
I agree, without knowing, we can only assume they will be worthless. I am in the US, Do you think discussion of this among employees is protected under the National Labor Relations Act, say in our company's private Discord channel?
I'm not sure. If you really want an answer, I'd post the question to Avvo and see what responses you get. I've found that you typically get written responses from real lawyers within 24 hours, and for generic questions like this, they don't ask for a paid consultation. IANAL and not related to Avvo in any way.
In the UK the total number of shares, and maybe the cap table (I don’t remember) is available from Companies House for a nominal fee, as part of the company’s annual accounts. No idea what the situation is elsewhere, sorry.