Shipping cost is not calculating for the rules applied

It is nopCommerce 4.5.0.

RE: " Form value count limit 2048 exceeded"  ... at ... SaveSelectedTabFilter

Are you using 3rd party Admin plugins?

You'll need to use the browser developer console (F12) to troubleshoot this.  Be on the Network tab.  Look at the request's Network tab, Payload sub-tab, Form data.  What Form Data do you see?  When I submit a "Add new" , the page is RateByWeightByTotalList, and I see this Form Data

draw: 8
columns[0][data]: StoreName
columns[0][name]:
columns[0][searchable]: false
columns[0][orderable]: false
columns[0][search][value]:
columns[0][search][regex]: false
columns[1][data]: WarehouseName
columns[1][name]:
columns[1][searchable]: false
columns[1][orderable]: false
columns[1][search][value]:
columns[1][search][regex]: false
columns[2][data]: CountryName
columns[2][name]:
columns[2][searchable]: false
columns[2][orderable]: false
columns[2][search][value]:
columns[2][search][regex]: false
columns[3][data]: StateProvinceName
columns[3][name]:
columns[3][searchable]: false
columns[3][orderable]: false
columns[3][search][value]:
columns[3][search][regex]: false
columns[4][data]: Zip
columns[4][name]:
columns[4][searchable]: false
columns[4][orderable]: false
columns[4][search][value]:
columns[4][search][regex]: false
columns[5][data]: ShippingMethodName
columns[5][name]:
columns[5][searchable]: false
columns[5][orderable]: false
columns[5][search][value]:
columns[5][search][regex]: false
columns[6][data]: DataHtml
columns[6][name]:
columns[6][searchable]: false
columns[6][orderable]: false
columns[6][search][value]:
columns[6][search][regex]: false
columns[7][data]: Id
columns[7][name]:
columns[7][searchable]: false
columns[7][orderable]: false
columns[7][search][value]:
columns[7][search][regex]: false
columns[8][data]: Id
columns[8][name]:
columns[8][searchable]: false
columns[8][orderable]: false
columns[8][search][value]:
columns[8][search][regex]: false
start: 0
length: 15
search[value]:
search[regex]: false
SearchStoreId: 0
SearchWarehouseId: 0
SearchCountryId: 0
SearchStateProvinceId: 0
SearchZip:
SearchShippingMethodId: 1
__RequestVerificationToken: ...

Hi Team,

Form Data is like this;

restrict_19: 237
restrict_20: 237
restrict_21: 237
restrict_22: 237
restrict_23: 237
restrict_24: 237
restrict_25: 237
restrict_1: 237
restrict_18: 1
restrict_19: 1
restrict_20: 1
restrict_21: 1
restrict_22: 1
restrict_23: 1
restrict_24: 1
restrict_25: 1
restrict_1: 1
restrict_18: 2
restrict_19: 2
restrict_20: 2
restrict_21: 2
restrict_22: 2
restrict_23: 2
restrict_24: 2
restrict_25: 2
restrict_1: 2
restrict_18: 3
restrict_19: 3
restrict_21: 3
restrict_22: 3
restrict_23: 3
restrict_24: 3
restrict_25: 3
restrict_1: 3
restrict_18: 4
restrict_19: 4
restrict_20: 4
restrict_21: 4
restrict_22: 4
restrict_23: 4
restrict_24: 4
restrict_25: 4
restrict_1: 4
restrict_18: 5
restrict_19: 5
restrict_20: 5
restrict_21: 5
restrict_22: 5
restrict_24: 5
restrict_25: 5
restrict_1: 5
restrict_18: 6
restrict_19: 6
restrict_21: 6
restrict_22: 6
restrict_23: 6
restrict_24: 6
restrict_25: 6
restrict_1: 6
restrict_18: 7
restrict_19: 7
restrict_20: 7
restrict_21: 7
restrict_22: 7
restrict_23: 7
restrict_24: 7
restrict_25: 7
restrict_1: 7
restrict_18: 8
restrict_19: 8
restrict_20: 8
restrict_21: 8
restrict_22: 8
restrict_23: 8
restrict_24: 8
restrict_25: 8
restrict_1: 8
........
........
..........
restrict_18: 247
restrict_19: 247
restrict_20: 247
restrict_21: 247
restrict_23: 247
restrict_24: 247
restrict_25: 247
restrict_1: 247
restrict_18: 248
restrict_19: 248
restrict_20: 248
restrict_21: 248
restrict_22: 248
restrict_23: 248
restrict_24: 248
restrict_25: 248
restrict_1: 248
restrict_18: 249
restrict_19: 249
restrict_20: 249
restrict_21: 249
restrict_22: 249
restrict_23: 249
restrict_24: 249
restrict_25: 249
restrict_1: 249
__RequestVerificationToken: CfDJ8Hkxi10tg4dNsg_VfWmoyVVq9K..........-nLK928r21cZAdU12A


Headers are like this;

Request URL:  https://www......com/Admin/Shipping/Restrictions
Request Method: POST
Status Code: 500 Internal Server Error
Remote Address: 199:.....:443
Referrer Policy: same-origin


What should be the issue?

Many thanks for helping

Shipping method restrictions are the country-specific  selections in which you want the shipping method(s) not available.  It seems that you have too many "choices" to be handled by the Form's implementation.  I suggest you first try to Unpublish several Countries from the Country List page  https://admin-demo.nopcommerce.com/Admin/Country/List.  
If it still does not work, then you may have to Delete some countries from that page.