How does the standardisation process in the EU work?
The CEN summarizes how they work on their website:
What we do ?
European Standards (ENs) are based on a consensus, which reflects the economic and social interests of 34 CEN Member countries channelled through their National Standardization Organizations. Most standards are initiated by industry. Other standardization projects can come from consumers, Small and Medium-sized Enterprises (SMEs) or associations, or even European legislators.
Put another way they let industry players work out norms that affect them between each other, with occasional input (or initiatives) from consumers, associations, or EU legislators. The EU legislator bit can at times mean "please work out a standard that works for you in short order or we'll make you comply with whatever norm we come up with" - like what happened when the EU insisted phone chargers should be interoperable when they wanted to cut electronic waste.
The CENELEC has similar language on their website. I'm not able to locate the same type of page for ETSI but to the best of my knowledge they also work the same.
Is the application of these standards the entirety of Single Market regulatory alignment for goods or is it only a portion of it?
The latter. Sometimes, industry players are happy with the status quo and don't want to change what they do (think safety standards, like bans of pesticides), or the EU has an agenda that goes against the will of industry players (think ecological transition, like the rollout of ever stricter emission standards for vehicles).