Yes, it is time to move your basil seedlings to a large growing space. I have seen basil thrive planted both individually and in groups in pots. You have enough seedlings to try both methods. The tricky part is disturbing the roots as little as possible during the transplanting process. I use kitchen silverware and tweezers to separate the plants. It is okay to hold the seedlings by the leaves. Avoid touching the stems since you can crush or break them very easily. After you have the seedlings in a new pot, water well to remove the air pockets and hydrate the stress roots.

I agree--they are ready to be transplanted. I generally do 2-3 seedlings in a 2 1/2" pot. As Chervil2 said, water well to pack the soil, and after a day or two, then they will also majorly benefit from a weak liquid fertilizer--bottom watering is best. Your seedlings are still at the cotyledon stage--they'll be getting their first real leaves soon (probably can see the pair already). At that point, they no longer receive food from the seed, which they've been living off of until now.

Also, basil seedlings do stagnate when not perfectly happy, especially if they're not warm enough. It's not unusual to see very little activity for a period, then a growth spurt. Yours also look like they're a little low on light--the bent stems reaching. You really need strong light right (1-2") above the seedlings to avoid legginess.