The clinical Hearing Aid feature on AirPods Pro 3 is subject to regulatory approval in each country, which is why it is not available in all markets. Singapore was not included in the initial launch countries for the over-the-counter hearing aid classification. This is because medical device regulations vary by country, and Apple needs approval from each country's health authority before offering the feature there.
As for what you miss out on without the full Hearing Aid feature: the main thing is the in-app audiogram hearing test and the clinically calibrated hearing amplification profile based on your test results. Without it, the AirPods cannot function as a prescribed or OTC hearing aid.
However, you can still use several related features in Singapore that may genuinely help with hearing. Conversation Boost is available and works independently of the hearing aid certification. It uses the AirPods' beamforming microphones to focus on the voice of a person in front of you and amplify it, which many people with mild to moderate hearing difficulty find helpful in one-on-one conversations. You can enable it in Settings > Accessibility > AirPods.
As for Hearing Protection, this feature works in the opposite direction. It monitors the sound levels coming through the AirPods and automatically reduces very loud audio to protect your hearing from sustained or sudden loud sounds. It is about prevention rather than amplification.
So while the full clinical hearing aid functionality is not available in Singapore yet, Conversation Boost is worth trying for your use case.