Visas for digital nomad in Singapore

You can't get any separate visa for this. You are only entitled for Singapore tourist visa, which is for 30 days, can be extended another 30 days (total 60 days).

For second time extension (another 30 days, total 90 days), very likely you won't get unless you have a valid reason like medical treatment in Singapore.

Note: Legally, you can't work in Singapore during your visit but you can continue work for your existing company under “work anywhere concept” located in another country, using remote desk. Good luck

In general, Singapore does not welcome foreigners that benefit from the country's environment without contributing to the local economy (in terms of work or business and tax).
As in most countries, you need a work visa to perform any paid work (including work solely for overseas clients or employers). Contrary to some other countries, where it is possible (but not legal!) to do this on a visit visa under the radar, in Singapore it is NEVER a good idea to break the rules - the consequences when found are just too grave!
And since a proper work visa is only available for employment with Singapore-registered companies (which your clients probably are not), your only option is registering a business and employing yourself in it (google the EntrePass) or investing in a local business (google the Global Investor Programme).
Also note that for stays below 6 months you cannot rent residential property, thus have to stay in (expensive) hotels.