Hopefully your employer will join the party and get the scheme and your investment sorted out.
I think that would be the best outcome for you.
However, I realise that this may drag it's heels and be a source of great anxiety for you.
If you contribute to the workplace pension scheme via salary sacrifice, you save paying (1) income tax & (2) national insurance, on the portion 'sacrificed'. It would be worth looking at NI rates for your level of income to understand just how much of a saving (.... which is a pension contribution) that translates to.
If you want to pay into a SIPP, this would be from your pay-packet after both income tax and NI had been deducted by your employers payroll team. However, the provider of the SIPP (eg Vanguard) would normally automatically reclaim the income tax from HMRC on your behalf, and add it to your SIPP - typically 8 weeks after you'd added your money. But you wouldn't get the National Insurance back, nor would you be getting the employers contribution.
Good luck getting things sorted out and don't let your employer away with it.