hmm. I've not had those STIs in pieces and the EV techdoc isn't at all helpful
https://si.shimano.com/pdfs/ev/EV-ST-R7020-4341B.pdfBut if you assume that the main pivot is built the same way as other recent STIs then it is retained by a snap ring (actually what is often known as an 'E' clip). This is usually silver coloured, in contrast to everything else in the pivot assy, and is usually positioned on the inboard end of the pivot. Normally the pivot is a sod to reassemble (there are springs....), but everything pivots on two Delrin bushings. I have occasionally bothered to replace worn bushings with some from a dead lever. Oddly enough if mineral oil leaks from the brake circuit or is spilt on the pivot, this can accelerate wear in the bushings.
But before delving into that, it should be noted that in most recent STIs both upshift and downshift levers couple with the index mechanism via two steel prongs just behind the levers. Normally there is about 1mm clearance between the levers and the prongs, so that there is some dead travel in the levers before the levers hit the prongs and initiate any movement in the index mechanism. Both levers are fitted with bias springs (near the top, hidden behind a small plastic cover) so that they are sprung (biased) outwards. If these springs fail to do their job, then the lever(s) are no longer biased outwards and there will be a terrible rattling sound as the levers bounce off the prongs as you ride down the road.
Thus I'd check very carefully that the bias springs are intact and working; compare with another 'good' lever.
cheers