Is it possible that I have too much money in savings accounts?

Well, of course. What you have been investing in, technically are low risks investments, hence the amount you are getting back isn't that much. If you would like to expand that, definitely SSB & REITs are good options, but TBH but are not attractive anymore..

I think it's definitely okay to hold on to more cash, and not deploy them just because you want to put it elsewhere. That clashes with investing as investing is about buying a business at fair value, not just because when you have the spare $ (might lead to overvalued/value trap at that point)

Absolutely. Even though many say you can never have too much of money, but I'd like to re-word that to you can never have too much of ASSETS.

Although cash is the most liquidable asset, it is not the highet return-generating asset.

In times where inflation peaks over your bank's savings account interest rate, your assets is in fact being eroded if you aren't able to generate a higher return as compared to inflation.

It is possible in your scenario. In fact many Singaporeans are in such dilemma. That said SSB and REITS which you have recommended are good avenues to start.

However should you progress and understand your own risk profile, pherhaps the STI ETF is one good method to park money, earn dividends over the long run while holding it

Totally possible, and I believe I'm the same situation as you (apart from cash held up in property) given that I have sold most of my stock positions.

Now that the rates are creeping down (esp my previous fav Citi Maxigain), its time to start re-investing.