Hi there,
1) You can save each of your surveys to your library and then make use of Reference Surveys in the Survey Flow. This will have all of the data collect in 1 survey project.
https://www.qualtrics.com/support/survey-platform/survey-module/survey-flow/advanced-elements/reference-surveys/
Be sure to add a Randomizer element and include the Reference Survey elements nested beneath that.
2) You can make a survey that functions like a URL randomizer. Within the 'URL-randomizer' survey, include a Randomizer element and End of Survey elements nested beneath them. Then, click Customize for each End of Survey element and Redirect to a URL for each of your 3 surveys. This will collect the data in 3 projects. Both options might look something like the below in the Survey Flow of the survey that is driving the randomizing.

All three surveys have been copied to the library now. This is where I currently am.
There is just one issue. Under 'Survey flow', I am missing the 'Reference survey'-option when adding an extra element.
This is how it looks like:
How come this is the case?

Hmm, it looks like you don't have the "Use Reference Blocks" permission enabled for your user. You're Qualtrics Administrator might be able to enable it for you.
Alternatively, you can make 3 blocks within your survey and then copy the questions from your 3 surveys into the Randomizer survey, each into their own block. Then, you can use the Randomizer element to show 1 of the blocks to respondents. At the bottom of each of the 3 blocks in the Randomizer survey, click "Import from Library" and then "Copy from Existing Survey". Search for the desired survey and then click on it. Select all the questions individually or select "Insert Entire Survey" to import all the questions/blocks from that survey. You can then set your Survey Flow up something like the below: