How does one spouse being highly compensated affect family FSA limits?

...is the dependent care FSA contribution limit for married filing jointly still $5,000?

Yes. A company specific limitation would not change the IRS caps.

(Paraphrasing:)

[Could] any shortcoming of the $5,000 contribution be made up on the second spouse's contribution?

Yes. Logically this must be true, because there is nothing preventing the second spouse from contributing the entire $5K to begin with. This would make the first spouse's HCE status irrelevant.

Side Note: If you do max out the FSA at $5K, there is still up to $1000 available for the Dependent Care Credit, if you have two or more children.

is the dependent care FSA contribution limit for married filing jointly still $5,000?

Yes.

Highly compensated employee (HCE) is relevant only for non-discrimination testing the plan. At a high level the purpose of non-discrimination testing is to ensure all employees benefit from the existence of the plan; a plan can't exist just to offer a tax benefit to HCEs. This testing is typically invisible to employees, unless the plan fails. If a plan fails there are various methods to remediate including assessing the tax in the contributions of the highly compensated employees. Some employers manage this risk by limiting HCE contributions up front.

This sort of goes to the interesting nuance of FSA plans. Your employer doesn't have to offer the maximum allowed by the IRS. But, the limitation would apply only to that plan. You and your spouse are free to participate up to the annual maximum; up to the limits being offered by plans you're eligible to participate in.

It's possible your employer has limited your contributions because you're an HCE. There is no IRS rule limiting your contributions based on your or your spouses income.

This isn't like a Roth IRA where your contribution limit phases out based on your income.