A couple of YouTube-specific things worth knowing:

Put the disclosure near the top of the description, not buried at the bottom — YouTube truncates descriptions after a few lines unless someone clicks "Show more," so if your disclosure is too far down, most viewers never see it, which risks non-compliance with FTC rules.
Also verbally mention it in the video if you're specifically recommending a product ("link in the description below") — this isn't strictly required by Amazon, but it's good practice and often expected for video content specifically.
YouTube also has a built-in "Paid promotion" / affiliate disclosure toggle in video settings (under Show More → Advanced Settings) — worth turning that on too, since it flags the video for viewers automatically.

On tracking IDs — this actually becomes more useful for you now, not less. Since everything is going through YouTube, you could still use separate tracking IDs per video (or per product category) to see which specific videos are driving the most purchases, rather than everything blending into one number.