Bulk import for Things is not implemented.
For bridges you are probably best off recreating those by hand. Just make sure to use the same IDs for the Things as is used in your text files.
For Things that are discoverable, I recommend just letting OH discover them. Set the Thing ID to the same as the IDs of the old text based Things and everything else should work just fine.
For Things that are not discoverable (e.g. HTTP, Exec, Generic MQTT, etc.) what you can do is manually create the Thing (again being careful to use the same ID), click the code tab, select DSL at the bottom and paste your text based config.
Make sure to remove the text based definitions for the Thing(s) you are working on before recreating them in the UI.
This approach lets you move slowly and deliberately, testing everything is working as expected as you go. This is why I recommend it.
But if you just want to do everything all at once and hope nothing breaks you can do the following.
Go to Developer Tools → API Explorer → things → GET all available things. Execute and save the result body in a text file somewhere.
Next remove your .things files.
Go to Developer Tools → API Explorer → things → POST things. Unfortunately you can only post one Thing at a time. So you’ll have to select one Thing’s JSON from the result you got on the previous step and paste it into the body for the POST call, execute making sure you get a 200 return code, and repeat for each remaining Thing.
The order of the JSON is not hierarchical meaning some Things will be created before their bridges. So using this approach you’ll likely not have a fully working config until you are done.
Of course, you can use a hybrid of this approach and the former approach, using the API only to recreate those Things that cannot be automatically discovered instead of pasting the definition into the code tab.
Now that OH has added a file converter to the API (i.e. translating between the internal JSON and the file based YAML and DSL config formats) it should be possible to implement an importer for Things similar to what already exists for Items. You can look to see if an issue is already open to add this (I think there is) but if not create one on the openhab-webui repo so this doesn’t get forgotten.