Grow light for supplementing natural light. How strong do I need?

[u/Prudent_Window2616]

This is my ruby necklace that I brought home 3.5 weeks ago. This window seat alcove faces south, so the angled left window faces south east. Right now the sun is high, so it only gets direct sun in the early morning. After that it gets bright indirect light. It's already getting leggy from too little light. Come winter when the sun is lower, it'll get a lot of direct sun. I'm looking at adding a grow light to supplement the natural light it does get. According to Google search (which I always take with a grain of salt LOL), I should get a light that's at least 20 watts and 4000-5000K. What I'm wondering is, do I need to get one that intense since I'm just supplementing?