Is ISO 17025 designed and intended to be implemented on individual, test-by-test basis?

ISO 17025 implementation applies to the overall activities of the laboratory, including for example personnel training or procurement. The “test-by-test” basis you refer to is applicable to the laboratory’s Scope of Work, for which accreditation is applied for. So you state what is being calibrated (including method and range); or what is being tested (analyte or group of analytes), in what matrix and using what method or instrument. An example is Heavy Metals in Soil by ICP-MS. For each method, yes you need to show technical competence to produce reliable, valid results. If your laboratory may is not involved with sampling, then you state in your documentation that sampling not the responsibility of the laboratory.

For more detail on what is required for ISO 17025, read the whitepaper Clause-by-clause explanation of ISO 17025:2017 available for download from https://advisera.com/17025academy/free-downloads/ and preview the ISO 17025 Academy toolkit at https://advisera.com/17025academy/iso-17025-documentation-toolkit/