Unable to erase eSIM's on iPad 4 and 5 (can't find: "Delete eSim" 'button').

Erasing an eSIM here would be unexpected, as neither iPad 4th or iPad 5th support eSIM.

About eSIM on iPad - Apple Support

For your cellular-capable models, look for and remove any nanoSIM found in the SIM slot.

Remove or switch the SIM card in your iPad - Apple Support

Related:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Neither of those models support eSim, so there's nothing to erase. They pre-date the introduction of e-sims.

They may have physical SIM cards inserted, in which case you would want to remove them from the sim trays in each.

click here ➜ Remove or switch the SIM card in your iPad - Apple Support

bob7 wrote:

I'm responding here to Phil0124 as well, who also provided useful information.

Based on what you've both said, there is no data to erase.

I'm nearly certain I saw the cel numbers that were used with these iPads. I can't find those now; it's likely they were stored in settings prior to me deleting all data content and settings, however the carrier name still shows in settings. Is that because the SIMs display the carrier name even after deleting all data content and settings?

They may display the carrier name in Settings if they are locked to that carrier, or have a physical SIM card in them from that carrier.

In terms of these iPads being able to be used with cellular (by a new user):

1) Can the SIMs in these iPads be activated (by a new user) for use with Verizon?

Depends on the SIM card. Apple sim cards can be used with different carriers. Carrier specific SIM cards belong to the carrier and can only be used with the specific carrier. Apple SIM cards were available with the 5th gen iPad, but not on 4th generation iPad though.

2) Can the SIMs in these iPads be activated for use with another carrier ?

Again, depends on the SIM card, but generally it's better just remove the sim card and install one given to them by the carrier they want to use. There's no reason to want to use the existing SIM cards. Carriers can issue new SIM cards at no cost for new users.

I suggest you remove the SIM card from the iPad regardless before having somebody else use them and recycle them.

Do note, the 4th generation iPad is stuck at iOS 10.3.4, and can only use 3G cellular which is getting mostly phased out in most of the world so its hardly relevant since it will be mostly useless at this point.

bob7 wrote:

The reason I asked questions 1 and 2 would be so that someone I gave it to could potentially use it cellularly, without having to get a new SIM card (although that might be required). (I wasn't worried about any funny business going on.) Sorry to have not made that more clear.

If using cellular, they’ll need a SIM card from their carrier, as Apple SIM is no more.

Set up cellular data service on your iPad Wi-Fi + Cellular model - Apple Support

bob7 wrote:

I'm responding here to Phil0124 as well, who also provided useful information.

Based on what you've both said, there is no data to erase.

Apple does not store data in a SIM.

There is iPad data unrelated to the SIM to erase. See the previously linked “what to do” document to prepare it for trade or gift or sale.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

I'm nearly certain I saw the cel numbers that were used with these iPads. I can't find those now; it's likely they were stored in settings prior to me deleting all data content and settings, however the carrier name still shows in settings. Is that because the SIMs display the carrier name even after deleting all data content and settings?

There are telephone numbers associated with an Apple Account, and an iPad that has (or had) a cellular data plan has (or had) an SIM (or an eSIM, where available) for cellular data billing purposes. That plan may or may not still be active. That associated number is for data billing, and cannot make or receive cellular calls, and cannot send or receive SMS or RCS text messages.

In terms of these iPads being able to be used with cellular (by a new user):

1) Can the SIMs in these iPads be activated (by a new user) for use with Verizon?

Why would the iPad still have a SIM installed? For what you are doing, you will have already removed that.

2) Can the SIMs in these iPads be activated for use with another carrier ?

As you will have removed the SIM already, there is no issue here. Even if the SIM is still active, the SIM remains in your possession, having been removed by you. The SIM is not in the iPad, so it cannot be used by another.