Software not installed

See this Apple article: iPhone models compatible with iOS 12 ->iOS 15

iPhone models compatible with iOS 15.2 – Apple Support (UK)

What happens when you go to -> Settings -> General -> Software Update?

Check iPhone type -> Go to: Settings -> General -> About.

1.

You need about 7 GB device storage, to free up iPhone device storage see this Apple articles below:

If you need more space for an update on your iPhone, iPad, or iPod touch

If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support

How to check the storage on your iPhone, iPad and iPod touch

How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)

Clear Other storage on your iPhone or iPad

Clear Other storage on your iPhone or iPad - Apple Support

What's the difference between device storage and iCloud storage?

What's the difference between device storage and iCloud storage? - Apple Support

2.

Check the range of the mobile network, see this Apple article: If you see No Service or Searching on your iPhone or iPad

If you see No Service or Searching on your iPhone or iPad - Apple Support

3.

Check also the Wi-Fi network, see the following Apple articles:

Connect to Wi-Fi on your iPhone, iPad, or iPod touch

Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network

If your iPhone, iPad, or iPod touch won't connect to a Wi-Fi network - Apple Support

4.

See also the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad or iPod touch won’t update - Apple Support

5.

If they are On, turn Off Hotspot & VPN.