When the mining reward becomes much lower would that also lower the effect of the halving on the price and the sentiments of traders?
It is expected for the halving to be already mostly a psychological event.
We just need to look up the number how much volume of Bitcoin is traded daily on exchanges and how much is mined daily. Currently (6.25 BTC x (6 (Blocks per hour) x 24 hours x 28k / BTC = 25 000 000 USD of BTC mined daily). It's a very tiny amount.
And even then, we haven't taken into consoderation that some Bitcoin are traded P2P, which doesn't reflect on exchange volumes.
Halving is already mostly a psycological event.
And honestly, we need to admit that 3.125
BTC per block is very low:
Bitcoin's halving is reminding everyone once more, how truly scare Bitcoin really is.

So, important reminder for everyone how close we are already to Bitcoin's Halving.
Only 1 year to go.

If earning 3.125 bitcoin per block is very low, what then are we to say concerning the reward per block for other years that are still ahead after the 2024 halving comes and go??
It is very low compared to 50 BTC / block, 12 years ago.
But 12 years is a very long time and Bitcoin's price has increased a lot since Bitcoin had 50
BTC / block.
In 12 years from now, I expect Bitcoin's price to be much higher compared to where it is now.
And Block rewards will replaced by transactions fees over time, where transaction fees will become the main source of revenue for miners.