Those cells appear full of nectar/sugar water, which is clear.
Cells with eggs will have nothing but eggs. No liquid. The bees don't put royal jelly (looks milky) in the cells until just before or after the egg hatches into a larvae.
Check the size of the cells. Take a ruler, measure (with the mm side) 10 cells. Measure towards the bottom of the comb, not right at the top. At the top, they often fill larger cells with nectar only and then make smaller worker-sized cells about 2-3 inches from the top of the bar. If that is more than 55 mm, or 5.5 cm, then you have no laying queen. A hive with "pressure" to build cells for a laying queen will mainly make worker-sized, 51 mm- 54 mm for 10 cells.
Bringing in pollen - it should be like every other bee has pollen. This queen should be pedal-to-the-medal trying to lay. If it is once in a few, then they aren't serious about feeding brood. And... worker bees will lay eggs. Those eggs will require pollen to develop. They will become drones. It happens at a low level in every hive, usually the sisters clean it up. No queen, no motivation to stop this worker-laying behavior.
So.... you know now what to look for in a hive that is functional. If you only see nectar in the cells, there is no laying queen. It happens pretty frequently with a package install. Please check again, close to the center of the bee population in the combs. There should be eggs and larvae there. I hate to ask a beek to "poke" their hive too much, but time is of the essence if you have no queen. Check in the next 5 days at the latest. I bet you're expecting cold weather for this weekend too... so better to wait for the weather to improve to check. If you aren't sure what to look for, put out an SOS call to your nearest bee club. Someone might be able to come out and check, or take time to ask questions to be sure they have the full picture before making a recommendation.
It may be that once the comb was drawn, the queen took a day or two to get back into "shape", so you just missed the eggs with this visit. But this is the time to ask your package supplier what they can do for you if you have no laying queen. Probably the answer is "nothing", because for all they know you accidentally killed the queen. So being prepared to get a queen is something you can think about now, before you get a chance to go into your hive. There are mail-order options, and looking up local queen suppliers may also yield pay dirt. And asking your local bee club about getting a queen ASAP may prove fruitful too.
On a different topic, yes I recommend a journal or diary of sorts. Noting the following may be useful:
1. At the entrance: how many bees in 10 seconds, or is it about 1 second or less between bees? If no, but some bees are going in and out, that's low traffic and should improve. Also note how many out of 10 have pollen. And the time of day you made the note - you'll see later why this matters.
2. Once you first open the hive: what number bar is the furthest/deepest comb at? Is it well covered with bees (I use ++ when I can barely see the comb), or just some (I use + for more than 1/4 lightly covered)?
3. If you probed to the center of the combs, did you see eggs (cells look empty unless the light and your eyes are good), or larva (milky, then like a grub), or nectar (shiny)? I actually note that detail for each comb - was it MT (drawn but empty), N (nectar), Nw (new), CWB (capped worker brood), eggs or L (for larvae). I can be pretty detail oriented tho! It's not critical to note that level of detail, but whether you saw eggs/larvae is extremely important to note, because you may be working back from that date to figure out the last time the hive was queenright.
4. Note the date you fed too, if you just added sugar syrup during the visit to the hive.
About adding the sugar syrup: If the syrup is cooling to air temp, and that's below 50 degrees, the bees can't take it. This weekend, good luck keeping that syrup warm enougH! But the closer it is to the cluster, the better you will be. I don't even have a divider between the mason jar feeders and the last comb - I do have an empty bar tho. Just in case they start drawing out comb faster than I expect! And I'm only doing that because of the cold nights.
Also you can add a light scent to the sugar water - some anise extract (the stuff intended for food is fine, 1 drop per quart is almost too much...).
Keep us posted! Watching... ;/ hope all will turn out to be well, or you can correctly identify queenlessness and get a queen in there.