transformer – Clipping waveform before the full bridge rectifier: What could be the reason?

I have a small audio mixing console which is supplied by ±19 V AC from an external transformer. The transformer started making a buzz sound, so I opened it up (because it was also much easier to start from there) and checked the voltage on the secondary with and without load.

Without load I can see a fairly nice waveform:

With the load (mixing desk) the waveform gets somewhat clipped:

Does that look reasonable to you?

I plan to change the transformer because it looks rather worn out from the heat it usually produces, but I wonder if you’d suggest there are further problems past the secondary of the PSU (mostly the main capacitors after the full bridge rectifier) and that I should not change the transformer at all.

As I am a newcomer to fixing electronics issues on my own, if you have a suggestion for a good book on electronics servicing, please go ahead and suggest it.