From the limited information you have provided it is impossible to debug why your extension does not work on a specific site and does work on other sites

hi,
did a print_r on the retuncode of $wa->addInlineScript($script);
saw these first lines;

object(Joomla\CMS\WebAsset\WebAssetManager)#884 (5) {
["registry":protected]=> object(Joomla\CMS\WebAsset\WebAssetRegistry)#518 (4) { 
["dataFilesNew":protected]=> array(0) { } 
["dataFilesParsed":protected]=> array(6) { 
["media\vendor\joomla.asset.json"]=> string(30) "media\vendor\joomla.asset.json" 
["media\system\joomla.asset.json"]=> string(30) "media\system\joomla.asset.json" 
["media\legacy\joomla.asset.json"]=> string(30) "media\legacy\joomla.asset.json" 
["media\plg_system_guidedtours\joomla.asset.json"]=> string(46) "media\plg_system_guidedtours\joomla.asset.json" 
["media\plg_behaviour_compat\es5.asset.json"]=> string(41) "media\plg_behaviour_compat\es5.asset.json"

and saw these last infos::

["onWebAssetRegistryChangedAssetOverride"]=> object(Joomla\Event\ListenersPriorityQueue)#591 (1) { 
["listeners":"Joomla\Event\ListenersPriorityQueue":private]=> array(1) { [0]=> array(1) { [0]=> object(Closure)#878 (2) { 
["this"]=> *RECURSION* ["parameter"]=> array(1) { ["$event"]=> string(10) "" } } } } } 
["onWebAssetRegistryChangedAssetRemove"]=> object(Joomla\Event\ListenersPriorityQueue)#880 (1) { 
["listeners":"Joomla\Event\ListenersPriorityQueue":private]=> array(1) { [0]=> array(1) { [0]=> object(Closure)#607 (2) { 
["this"]=> *RECURSION* ["parameter"]=> array(1) { ["$event"]=> string(10) "" } } } } } } } } ["activeAssets":protected]=> array(1) { ["script"]=> array(3) { ["xx_weather0"]=> int(1) ["xx_weather1"]=> int(1) 
["inline.fdd212cdd0684aec80324a770a7a7748"]=> int(1) } } ["locked":protected]=> bool(false) 
["dependenciesIsActual":protected]=> bool(false) ["sortedAssets":protected]=> array(1) { ["script"]=> array(0) { } } } 

on my working system I get:

RECURSION* [parameter] => Array ( [$event] => ) ) ) ) ) ) ) ) [activeAssets:protected] => Array ( [script] => Array ( [js_weather0] => 1 [js_weather1] => 1 [inline.fdd212cdd0684aec80324a770a7a7748] => 1 ) ) [locked:protected] => [dependenciesIsActual:protected] => [sortedAssets:protected] => Array ( [script] => Array ( ) )

A small trick that can help.
First, don't forget this:

use Joomla\CMS\Factory;
use Joomla\CMS\HTML\HTMLHelper;

Then:

$wa = Factory::getApplication()->getDocument()->getWebAssetManager();
$wa->registerAndUseScript('vuejs','mystuff/vue.2.6.14.js', [], ['defer' => true], ['core']);
$wa->registerAndUseScript('myvuescriptname','mystuff/myvuescript.js', [], ['defer' => true], ['core']);
$wa->useScript('myvuescriptname');

• myvuescriptname is ... the name of the item
• mystuff/myvuescript.js is the location of the script
  As I work a lot with JS frameworks and dependant scripts, I had to find a solution and this one works for me.

Don't use $wa = Factory::getApplication()->getDocument()->getWebAssetManager(); if it's not really needed (for example in the view you can use $this->getDocument()....)

Also You don't need $wa->useScript(); because you use registerAndUseScript already.

@jschmi102 I tried to make your comment more readable but didn't was really successfully, can you repost with correct styling and maybe not use print_r instead use var_dump or at least pretty copy-paste please.

hi,
what do you think?
If you have an application which runs perfectly with 5 systems and does not wit one singel system. Woluld you think the application is the problem orr the failing system?

So I did the most reasonable: I used a working backup/restore of the failing sytem. And what happened? My extension is working now on this system.