Hey, I did some more digging.
I found some log entries that were written at the moment the backup job threw the "body timeout error". (Those blocks of log entries appear for all VMs that show this problem).
grep -i "VM.export" xensource.log | grep -i "error"
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 HTTPS 192.168.60.30->:::80|[XO] VM export R:edfb08f9b55b|xapi_compression] nice failed to compress: exit code 70
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] [XO] VM export R:edfb08f9b55b failed with exception Server_error(CLIENT_ERROR, [ INTERNAL_ERROR: [ Unix.Unix_error(Unix.EPIPE, "write", "") ] ])
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] Raised Server_error(CLIENT_ERROR, [ INTERNAL_ERROR: [ Unix.Unix_error(Unix.EPIPE, "write", "") ] ])
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 1/16 xapi Raised at file ocaml/xapi/stream_vdi.ml, line 127
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 2/16 xapi Called from file ocaml/xapi/stream_vdi.ml, line 307
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 3/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 24
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 4/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 39
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 5/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 24
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 6/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 39
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 7/16 xapi Called from file ocaml/xapi/stream_vdi.ml, line 263
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 8/16 xapi Called from file list.ml, line 110
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 9/16 xapi Called from file ocaml/xapi/export.ml, line 707
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 10/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 24
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 11/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 39
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 12/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 24
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 13/16 xapi Called from file ocaml/libs/xapi-stdext/lib/xapi-stdext-pervasives/pervasiveext.ml, line 39
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 14/16 xapi Called from file ocaml/xapi/server_helpers.ml, line 75
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 15/16 xapi Called from file ocaml/xapi/server_helpers.ml, line 97
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace] 16/16 xapi Called from file ocaml/libs/log/debug.ml, line 250
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|VM.export D:6f2ee2bc66b8|backtrace]
Nov 4 08:02:33 dat-xcpng01 xapi: [error||141766 :::80|handler:http/get_export D:b71f8095b88f|backtrace] VM.export D:6f2ee2bc66b8 failed with exception Server_error(CLIENT_ERROR, [ INTERNAL_ERROR: [ Unix.Unix_error(Unix.EPIPE, "write", "") ] ])
daemon.log shows:
Nov 4 08:02:31 dat-xcpng01 forkexecd: [error||0 ||forkexecd] 135416 (/bin/nice -n 19 /usr/bin/ionice -c 3 /usr/bin/zstd) exited with code 70
Maybe this gives some insights 
To me it appears that the issue is caused by the compression (I had zstd enabled during the backup run).
Best regards
//EDIT: This is what ChatGPT thinks about this (I know AI responses have to be taken with a grain of salt):
Why would there be long “no data” gaps? With full exports, XAPI compresses on the host side. When it encounters very large runs of zeros / sparse/unused regions, compression may yield almost nothing for long stretches. If the stream goes quiet longer than Undici’s bodyTimeout (default ~5 minutes), XO aborts. This explains why it only hits some big VMs and why delta (NBD) backups are fine.