Currently, I'm using LS 5.6.27 and paid ComfortUpdate, but it says that my LS installation is up to date. How can I update to LS 6.x?

As LS5 and LS6 are different branches and both are supported, it is correct that your installation is "up to date".

However, if you go into "Comfort Update" on your installation you should see the option to update to LS6.

However, I just looked at my own LS 5.6.27 and it did not offer me to upgrade to LS6. But I remember that I got offered the upgrade to LS6 by ComfortUpdate before my last update.

However, today your LS 5.6.27 is actually NOT up to date anymore. I got the option to upgrade to LS 5.6.28. But even after the update to 5.6.28 there was no option to upgrade to LS6.

I think you can create a bug report, or as you are a paying customer of Comfort Update you can open a support ticket (don't let first level support tell you that you can't get support for Community Edition, if you are a paying customer of Comfort Update. They sometimes tend to do this).

Got some feedback and seems like there is currently no way to upgrade from LS5 to LS6 via Comfort Update (only updates from LS6.x to LS6.x).

I got no feedback if there are plans to make an upgrade path from LS5 to LS6 via Comfort Update at any point in time. Currently you will need to upgrade manually.

So if you have further questions about Comfort Update, I recommend to open a support ticket, as you are a paying customer of Comfort Update. CU is provided by Limesurvey GmbH and only they can really do something about this.

So sad, thank you.