Set the header block to be the first element in the top.links block

I am facing this issue in magento 2.3.4:

I want the welcome message to be the first element in the top.links block.

Now it is looking like this:

For that, I have made some changes inside design/frontend/{company name}/{theme name}/Magento_Theme/layout/default.xml and now it looks like this:

<move element="top.links" destination="top.link.header"/>
<move element="header" as="header" destination="top.links" before="-"/>
<move element="my-account-link" destination="top.links" after="header"/>
<move element="authorization-link" destination="top.links" after="my-account-link"/>
<move element="register-link" destination="top.links" after="authorization-link"/>
<referenceBlock name="catalog.compare.link" remove="true"/>
<referenceBlock name="wish-list-link" remove="true"/>

The line of code that should move the welcome message to be the first, is <move element="header" as="header" destination="top.links" before="-"/> but for some reason, it fails and I don’t understand why.

Does anyone has a suggestion on how to solve this?

Edit:
I’ve noticed that the welcome part is the last to be loaded. Could that mean something?