There isn’t really a one size fits all solution, it’s just a matter of what you prefer to best achieve for the outcome you are after. Sealing and non-sealing the grout will both have it’s flaws and benefits.
As per Kevbos above, you can already buy the grout with premixed sealer. These are flexible with stain resisting and adds strength to the grout bonding, however, additives can also be bought to mix with the cement grout for further prevention of moisture penetration below the tiles.
Since you have already finished the grout, just check to ensure that it already had the premix of seal included, otherwise you will either need to cut out all the hard work on grouting that you did and redo with premix sealer/additives, or simply just apply simple brush on sealants to the grout to finish your job per the question you are raising as there is nothing worse then having to redo the hard work that you already did. I’m not saying that grout sealer is good or bad, but if you already applied a grout that has no premix then move onto the next step and finish off with top sealer. In fact there are some brush on water-based sealants out there that are suitable for grout sealing which can also be brushed on tiles including the grout to assist water beading to minimise soap/scum buildup and leave your tile and grout looking clean and tidy for a while.
From personal experience, if you are living in an already established home which you plan living in for a long time, then avoid using a top-coat for grout sealing, just purchase the grout with already premixed sealer and if necessary buy some additives to improve the strength/flexibility/staining of the grout. But for new homes, yes I would definitely do this including the top-seal.
Why wouldn’t I want to top-seal for established homes you may be asking, it’s purely because I would want to identify any leaks early rather than late. When you top seal grout you are in fact trapping any moisture built below the tiles over time, and moisture needs to release into the air. When you trap any small buildup of moisture below the tiles then further down the track this can cause some serious moulding issues in your place not to mention other bad damages that will progress to affect the structural integrity of your home. Yes, top-coat sealant is good, but it is only as good as it can be if the area you are protecting is practically 100% waterproof behind the tiles, and I don’t think I need to say this but with building movements at joins and barriers failing due to excessive weight loads, nothing I find is actually genuinely waterproof, even membranes fail from a small disturbance to buildings which’ll give way for water to seep through.
I hope I have answered some of your questions. Please note I am not a professional tiler, but I have been working alongside tilers for over 25 years in the construction industry.