I found a bad starter on the compressor, but when I went to look up the parts to order, they were different than what I was removing, and there was no indication that it was a sub. To be specific, the part I removed was a combo starter/overload numbered with 513604045 which points to WR07X10097. The parts in the parts list show a separate starter and overload, wr07x10084 and wr08x10025 respectively. I did install the listed parts, and the compressor seems to be working fine.

Why is there a discrepancy between what I found on the machine and what the parts list shows? Customer says it has never been worked on before.

The parts I installed are the ones that show on the parts list through the vendor that sold them to me, and another vendor that I use, and even Sears, #733 and #735 on the sealed system page. In other words, three different resources all point to the discrete parts that I installed as correct.

Even Embraco has a compressor booklet online that says "TSD-150v" as the starting relay type.

Please help me understand how you came up with the combo unit as the correct part. I will go back and replace it.

Check to see if the compressor is Embraco or Samsung. If Samsung, or other foreign type, you might be ok: they use an impedance protected one, while all the Embraco's I have seen are not, and you must use the packaged start device.

The compressor is an Embraco EGX70HLC.

I checked different sites, one says "unknown" others specify the part WR07X10084
They can't all be wrong, so you are probably ok.
Just tested a GE compressor similar to yours. Start winding only drew 7 amps with 115 volts applied. Real power dissipated only about 380 watts for both windings. Compressor survived and any extended power period will be terminated by the Klixon.