Why an old machine is less of a problem than it used to be
The processing a synthesizer needs has not grown much in fifteen years - an oscillator, a filter and an envelope cost roughly what they always did, while processors got several times faster. What grew is everything around them: sample libraries measured in gigabytes, plugin suites that scan for a minute on launch, project templates that load forty instruments before you have played a note. A 2018 laptop can run a great deal of music software. It struggles with the accumulated weight of a modern installation, which is a different problem.
Where the browser genuinely helps
No installer, no disk footprint, no plugin scan, no background updater, no licence service. Audio processing itself runs in the browser's native audio code, so the cost of an oscillator or a filter is comparable to a desktop instrument doing the same job - the saving is in everything that is not audio. On a machine where disk space and boot time are the real constraints, that is most of the problem removed. The engineering detail is on the browser-based DAW page.
And where it does not
A browser has its own memory overhead, and if the machine is already at its limit from open tabs, adding a studio to them will not go well. Very high voice counts will find the ceiling faster than a native application would. And nothing loads without a connection. If the machine is weak and usually offline, an installed lightweight DAW is the better answer and several good ones cost nothing. The full set of trade-offs is on the make music anywhere hub.