If my spouse is contributing to their TFSA and RRSP, does that have any impact on my contribution limits?

No. Under the TFSA and RRSP rules, each person has their own contribution limit and is tracked separately by CRA.

It is your spouse’s responsibility to ensure any contribution made does not exceed their limits under the Income Tax Act. Your spouse is solely responsible for any taxes or fines imposed if contributions exceed the TFSA or RRSP limits.