The cantonal social security administration/ compensation fund normally determines whether a person is eligible for self-employment status.
I reviewed the self-employment application form for SVA St. Gallen, where you would likely apply. Answers to questions in section 12 will likely determine whether self-employment status is granted:
https://www.svasg.ch/online-schalter/pdf/form_1010r.pdf
Below is a translation of section 12 to assist you:
"12. Remarks on the social security legal position
A person is self-employed if he/she is active in his/her own name and on his/her own account as a free entrepreneur. The intention to take up a self-employed activity is not sufficient for recognition as a self-employed insured person by the compensation fund. Recognition as a self-employed person requires that the insured person is already engaged in a meaningful activity that is relevant to the business. The assessment of the social security status is based on documents that must be enclosed with this registration form. The following documents are meaningful:
-Offers and invoices to customers
-Proof of invested equity capital
-Signed contracts with customers
-Description of the self-employed activity
-Rental agreements for business premises
-Bookkeeping
-Leasing or purchase contracts for investments
-Other documents proving the independent activity
I act on behalf of my client towards my clients Yes No
I invoice my customers directly Yes No
I bear losses in case of insolvency of my customers myself Yes No
I have my own business premises with facilities that are customary in the industry Yes No
I am bound by instructions of the client (working time, reports) Yes No
I bear expenses myself Yes No
I procure the necessary material on my own account Yes No
I have already taken up self-employment Yes No
I had to make investments for my job. yes no
If yes:
Type of investment
Costs CHF
My earnings consist of a commission Yes No
If yes, from which companies
I work for the following number of clients
1
2 – 3
4 – 6
more than 6"
There is a list of possible enclosures at section 16 which is also important (translated):
"16. Enclosures
Offers and invoices to customers
Proof of invested equity capital
Contracts signed with customers
Description of self-employment
Rental contracts for business premises
Accounting
Lease and purchase contracts for investments
Other"
I would suggest completing the SVA St. Gallen form completely and honestly. Also, if this is a "side-gig", you should likely check the Nebenerwerb box in section 6.
Good luck!