OMG Seriously, have you never heard of Escher!

Oh dear, I really hope you are making a joke I'm missing.

I suspect nobody really cares, but this is the sort of thing that has 'reduced' my interest in replying to posts here.
Dave answered a question as fully as possible with the info given and correctly asked the OP to give more info and correct their profile as that information is needed for us to help them.

And what happens.
Two sad bastards click the thumbs down button.
I can assure you the beards really do make you look like counts.

I zoomed in as best I can

I was quite grumpy earlier.
Here is a very quick example of how a shape can be bent using Radial Bending.

Tap ctrl to continue through, then intersect faces and delete the parts you don't want. And orient the faces.

Looks good, I made my minor criticisms elsewhere.

Times change.
In the past I would have given you a gif that showed you how to finish your project in less than 2min.
But then as an advanced user you should already know.
Your signature shows you are making money from this.
So, no.
But it is simple.

You don't need the c just tap ctrl and a small cross appears next to the pushpull tool, tap it again to turn it off.

If you don't want to be reminded there is an update you can turn the prompt off in Preferences/General

I agree with Dave, it looks like you are hiding actual faces which is not good modeling. Too easy to lose them, they obstruct visually if you have hidden geometry turned on and so on.
You should be using groups and components and Tags, hiding is something generally avoid.
The Option to hide rest of model or hide similar etc and turning on and off tags is a much better workflow.

Like Dave I'm a little curious, you can turn on hidden geometry to see the smoothed edges without seeing the hidden objects, they have two different tick boxes in View.

Without seeing the model my guess would a scale issue. Related to the tiny face issue.
The more detailed the Sphere the shorter the edges become the more likely the edges are to fail to form.
But by scaling up you may get it to work. Failing that you can draw in the missing edges.

I haven't downloaded either model to check, but the screenshots suggest that there may be a very long border edge.
Sketchup has a segment limit at which it will fail, no bugsplat, it just shuts down if you go over that limit, I think it is 10000 segments, 9999 will work but go 1 over and it just shuts down.
I could be wrong on the 10000.

You can try signing out and then back in again before you leave the office. The idea being it shouldn't need to check again for 28 days.
However this is not always guaranteed to work. Sometimes it just needs to do it continuously.
While on site if you have access to a wifi network or can connect your laptop using your phone you should be able to sign in and be good to go, until it decides otherwise.

I hate this system with a passion. My wireless connection is cellular and can be somewhat flaky and the number of times I have had to sign out and back in while actually in the middle of work is very aggravating. Just opening a second instance of SU can be enough for it to decide I'm not signed in.

If I was doing a lot of sitework these days I would probably keep a pre subscription copy on my laptop. Something that uses the older classic license, but even that I'm not so sure of.

One thing I see from your screenshot is that you must have the display settings way above normal, the text doesn't fit in the box and the tiny crosses are huge.
How this may be affecting things I don't know.

This is it in Real Time

This has been mentioned elsewhere and is being looked into. It hasn't been determined which specific combination of OS and Graphic card have the issue.
The people I have read with the problem usually only need to adjust the trays slightly for them to work properly, annoying but not fatal.

You asked the question 'over there' after we had both replied to you here.
I have now replied to you 'over there' and will add the related gif here.
The context menu offscreen is Explode.

You can basically use any image as a material in Sketchup, even a transparent png.
So you could use Tigs Section cut face and add a hand drawn transparent hatch to that if you want.