(edited after edited question)

In the WordPress block editor (Gutenberg), for every block you add, there is the option to add a CSS class. It’s the very last option in the block settings (while that block is selected). So add any term there, for example “mynewtable1”.

Then open the theme customizer (menu Design > Customizer in the left admin sidebar), in there the field for “custom CSS”, and add two css rules like this:

.mynewtable1 {
  border: 3px solid black;
  border-collapse: collapse;
}
.mynewtable1 td, .mynewtable1 th {
   border: 1px solid #999;
}

The first rule will create the thicker border around the table and make sure cell borders won’t double, the second one is for the cell borders themselves.

Choose whatver border thickness and color you like in there.
This should do the trick…

ANOTHER ADDITION:

If you want this to work for every table, forget about the class and just insert the following rules in the customizers custom CSS field:

table {
  border: 3px solid black;
  border-collapse: collapse;
}
td, th {
   border: 1px solid #999;
}

EDIT: My apologies I didn’t see this:

This solution wouldn’t work either because I have multiple tables going forward.

In order to generate a border on every table, you would need to use javascript.

document.querySelectorAll('table').forEach(el => {
  el.style.outline="2px solid black"
)}

Original response

You need to add a css style to the table, which can be done directly (inline) as follows:

<table class="has-subtle-pale-blue-background-color has-background" style="outline: 2px solid black"> 

Alternately, you could add a css style like this:

<table class="has-outline has-subtle-pale-blue-background-color has-background">

And then in your css file:

.has-outline {
    outline: 2px solid black;
 }

Of course, 2px width and black is just as an example and you can set those values to whatever you like.

I tried adding a table on a WordPress site by using the gutenberg editor.

The table has the following code:

<figure class="wp-block-table aligncenter is-style-stripes">
   <table class="has-subtle-pale-blue-background-color has-background">
      <thead>
         <tr>
            <th class="has-text-align-center" data-align="center">Heading1</th>
            <th><strong>Heading2</strong></th>
         </tr>
      </thead>
      <tbody>
         <tr>
            <td class="has-text-align-center" data-align="center">text1</td>
            <td>value1</td>
         </tr>
         <tr>
            <td class="has-text-align-center" data-align="center">text2</td>
            <td>value2</td>
         </tr>
         <tr>
            <td class="has-text-align-center" data-align="center"></td>
            <td></td>
         </tr>
      </tbody>
   </table>
</figure>

How can I add a border to this table? Google points to a huge range of plugins centered around wordpress tables and I absolutely do not want to add one more plugin to my site for something as simple as a table.

Besides the plugin solution all other solutions that I’ve come across instruct to edit the HTML code and add a code in every <td> tag for a border. This solution wouldn’t work either because I have multiple tables going forward.

How can I add a table to WordPress that contains a border between all cells and which contains a strong external border all around the cells?