am I as a small business required to complete this questionnaire

It is usually not mandatory, but neither is it entirely optional

No, a small business is in most cases not legally obliged to complete this list. The CSRD (Directive (EU) 2022/2464) imposes reporting obligations on large and listed undertakings, not on SMEs. If the list you have received is based on EFRAG's VSME standard, that is precisely what the name says: voluntary ("Voluntary"), intended for unlisted SME undertakings that are asked for information by a larger customer.

Completing it voluntarily does not mean it is without consequences for the relationship. Your customer is probably asking for the list because they themselves fall under the CSRD and need to map their supply chain. Refusing may then affect the commercial relationship, even without a legal obligation. What you usually do have on hand in the VSME basic module are the factual data: the number of employees and the countries where you have establishments are usually already in your own records and are not a matter of contention. Where things more often get stuck are qualitative questions about policies or objectives that you have not yet formalised — there you can factually answer "no, not yet" or "in development", without this being scored or assessed anywhere.

Basis: CSRD scope versus VSME voluntariness

The distinction follows directly from the scope provisions of Directive (EU) 2022/2464, which links the reporting obligation to size criteria that a small business typically does not meet, and from the status of the VSME itself as a voluntary framework from EFRAG for undertakings that fall outside that scope but are nonetheless asked for information by chain partners. Note: this is separate from obligations that may directly apply to you, such as the basic registration under the Trade Register Act 2007 or, in another list, the ten measures of Article 21(2) NIS2 — the latter concerns cybersecurity rather than sustainability.