Yep. 38mm deep front.
125cm of records weigh approx 91kg. Sagulator my shelves will sag by 1.2cm.
I may add a few basic cut down broom handle supports per shelf. It will probably be better for the records if they are not leaning against each other too.
I built the base cabinets fairly strong so I didn't have to use the wobbly internal lath and plaster wall to support any weight.
There is a cladding on the back wall with some carpet underlay behind to help with sound proofing.
Heres the before: