Please provide a diag file. See documentation howto do this.
Please have a look at the entity ids. They should contain the serial number of the hp. If not and the ids are only .luxtronik2_ your installation is broken and you have to remove the devices and re create them.
BUT VERY IMPORTANT: You will lose your sensor history and all links to them (dashboards, scripts, automations and so on)!

The entities are OK. however, both the .luxtronik2_xxx_0512 and the .luxtronik2_xxx_013 entities are displayed under the same device.

[Update]:
It is not possible for me to download diagnostic data. Neither with “edge”, “safari” nor with “brave”.
With other integrations the download is possible without any problems.
Have found and solved the problem.

@Guzz-T Strange...
Please have a look into the two file .storage/core.config_entries and .storage/core.device_registry.
Check the luxtronik ids are correct linked. If not you can backup the files, shutdown ha and correct it manually.
Alternative attach the files in the issue.

Here are the (shortened) files:

core.config_entries.json
core.device_registry.json
core.entry_registry.json

I assume:

• core.config_entries is correct
• in core.device_registry:
  • config_entries should only contain one entry
  • in xxx_013_heating primary_config_entry is wrong
• in core.entry_registry:
  • in luxtronik_xxx_013_outdoor_temperature device_id is wrong

Please note that I have tried the setup several times and each time it did not work properly.

[Update]:
It seems that the manual changes in the files are overwritten again by HA

I have now managed to create the diag files:
config_entry-luxtronik2-01JBFDSPEZEJB9ZMNGZBBZA0VQ.json
config_entry-luxtronik2-01JBFDD1J31QPAYDNZ1SJMGKNR.json

Please note that i am using the latest version of Bouni/python-luxtronik commit ceed16e5486e689e06fe88f3e908cdcc21f37dfe. However, I think that this has no influence on the setup of the HA components.

Here is the debug protocol of the setup:
debug_protocol.txt

I guess:

• Is there a continue missing after lux_helper.py#L85?
• It may be necessary to loop through all the heat pumps found at config_low.py#L256
• class fields should be fields of the created instance. See coordinator.py#L74ff

[Update]
With the changes mentioned, it seems to work.