There's basically zero chance 100Ω resistors are contributing to your issues on a protocol that is host-clocked and can operate in the single kilobaud range.

Lower speed or try one of the other fifty debug firmware projects.

https://github.com/raspberrypi/debugprobe

https://github.com/bugadani/rusty-probe-embassy

https://github.com/probe-rs/rusty-probe

https://github.com/ciniml/rust-dap

https://github.com/ccattuto/rp2040-dap-probe

Not all firmware implements all modes or the CMSIS-DAP spec correctly (most don't implement JTAG, either.)