Beginning with 2023, the SECURE 2.0 Act allows employer contributions to be Roth contributions. However, few 401(k) plan agreements have been modified to allow these, so most plans still require that employer contributions are pre-tax, particularly since the IRS has not issued any guidance on how the employer is to report employer Roth contributions on your W-2 so that you can be taxed on them. Any employer contributions made before 2023 were required to be pre-tax as Opus 17 said, so most, if not all, of your employer's contributions are indeed pre-tax.
The only way to have gotten the pre-tax funds into the designated Roth account in your 401(k) is to have done In-plan Roth Rollovers which would have been reported on Forms 1099-R with code G in box 7. Given that you haven't mentioned anything about doing IRRs, it does seem that the plan is correct that all of the employer contributions are pre-tax.
You can move the pre-tax funds to a traditional IRA by direct rollover and continue to defer that income or, as you indicated, you can roll them directly over your Roth IRA and pay the tax. Direct rollovers where the funds are paid directly to the IRA avoid the 20% mandatory tax withholding.
