Looks like it's possible after all using the bash operator <<<. This shell command works as intended:

shortcuts run "Test Alert" <<< "My Text Input"

"man bash"

 Here Strings A variant of here documents, the format is: <<<word The word is expanded and supplied to the command on its standard input. 

Update 1: per @Martin R.'s comment above, the following construction also works.

echo "My Text Input" | shortcuts run "Test Alert"

Looks like it's possible after all using the bash operator <<<. This shell command works as intended:

shortcuts run "Test Alert" <<< "My Text Input"

"man bash"

Here Strings
A variant of here documents, the format is:

 <<<word 

The word is expanded and supplied to the command on its standard input.

Update 1: per @Martin R.'s comment above, the following construction also works.

echo "My Text Input" | shortcuts run "Test Alert"

Looks like it's possible after all using the bash operator <<<. This shell command works as intended:

shortcuts run "Test Alert" <<< "My Text Input"

"man bash"

 Here Strings A variant of here documents, the format is: <<<word The word is expanded and supplied to the command on its standard input. 

Looks like it's possible after all using the bash operator <<<. This shell command works as intended:

shortcuts run "Test Alert" <<< "My Text Input"

"man bash"

 Here Strings A variant of here documents, the format is: <<<word The word is expanded and supplied to the command on its standard input. 

Update 1: per @Martin R.'s comment above, the following construction also works.

echo "My Text Input" | shortcuts run "Test Alert"