As next step I tried the firmware binaries from http://thehackbox.org/tasmota/020500/. Because of the MQTT error I made a custom build with a MQTT Keepalive of 30 seconds. This changed the log a bit:
1547307857: Received PINGREQ from sonoff-workbench
1547307857: Sending PINGRESP to sonoff-workbench
1547307867: Received PINGREQ from sonoff-workbench
1547307867: Sending PINGRESP to sonoff-workbench
1547307877: Received PINGREQ from sonoff-workbench
1547307877: Sending PINGRESP to sonoff-workbench
1547307887: Received PINGREQ from sonoff-workbench
1547307887: Sending PINGRESP to sonoff-workbench
1547307897: Received PINGREQ from sonoff-workbench
1547307897: Sending PINGRESP to sonoff-workbench
1547307908: Received PINGREQ from sonoff-workbench
1547307908: Sending PINGRESP to sonoff-workbench
1547307919: Client sonoff-workbench already connected, closing old connection.
1547307919: Socket error on client sonoff-workbench, disconnecting.
1547307919: New client connected from 192.168.130.33 as sonoff-workbench (c1, k10, u'sensors').
1547307919: tele/sonoff-workbench/LWT
1547307919: Sending CONNACK to sonoff-workbench (0, 0)
1547307919: Sending PUBLISH to homeassistant (d0, q0, r0, m0, 'tele/sonoff-workbench/LWT', ... (7 bytes))
1547307919: Received PUBLISH from sonoff-workbench (d0, q0, r1, m0, 'tele/sonoff-workbench/LWT', ... (6 bytes))
1547307919: Sending PUBLISH to homeassistant (d0, q0, r0, m0, 'tele/sonoff-workbench/LWT', ... (6 bytes))
1547307919: Received PUBLISH from sonoff-workbench (d0, q0, r0, m0, 'cmnd/sonoff-workbench/POWER', ... (0 bytes))
1547307919: Received SUBSCRIBE from sonoff-workbench
This time the MQTT server doesn’t abort the connection because of a timeout (because it’s bigger now). Instead the Sonoff opens a new connection (because the old one died silently). My WiFi isn’t flacky in general. There is no raeson for delays >10 seconds. As next step I tried the SDK 3.0.0 / STAGE. This doesn’t solve the issue, too.
As last step I’m using the suggested Core 2.3 build as @Bieniu suggested. This is the same Core as my previous setup with Tasmota 5.12. Hopefully it will solve the issue. This is a nice write up for toubleshooting: https://github.com/arendst/Sonoff-Tasmota/wiki/Troubleshooting#wifi-issues-arduino-core-versions-and-expressif-sdk