Hi, I also have a private medical insurance ( HSF) via my employer. From my experience, any counselling sessions are highly confidential.
Please, definitely reach out for help. Do you need to go via HR or can you just contact the insurance directly? You can also mention that you are looking for Counselling sessions due to a private matter ( if need to go through your employer’s channels). The rest will be confidential, where only your counsellor will be aware of the situation.
In my case, the info was never shared between my employer and medical insurance. I just called my private healthcare and had an initial session over the phone and had 6 sessions with a new designated counsellor after that. They tend to outsource the Counselling Service. I have a bit of knowledge on how this is done as used them every year and my Counsellor explained how this works.
Please look after yourself. Employment laws are quite strict, and the company must support you. I understand, however, that sharing info with the employer can be counterintuitive ( I did not). Regarding serious self-harm, any Counsellor has a duty of care to share this information, but it has to be something very serious.
Also, please check if you can upgrade your employer’s cover with the health insurance directly for a better cover and more options. However, even a basic cover should cover the counselling services.
My experience with GP was generally positive too, however, they tend to prescribe antidepressants and treat the symptoms, rather than treating the underlying cause.
I hope you have a good solution soon. Maybe a holistic approach ( both GP and private route) would work the best.
Sending love!