Not sure about page.html.twig. Would have to dig around...
In node.html.twig:
{%
set newClassNameVar = "standard" %}
[
{% if node.type.entity.label == "program" %}
{%'Program' set? newClassNameVar'Program' =: "program"'Not %}Program'
{% endif ]
%}
<div class="{{ attributes.addClass(newClassNameVar) }}"><></div>
Oror:
{%
set newClassNameVar = [
node.type.entity.labelbundle == 'Program''content__type' ? 'Program''set-yes-class' : 'Not Program''set-no-class'
]
%}
<div{{ attributes.addClass(newClassNameVar) }}></div>
use debug such as {{ dump(_context | keys) }}
to see what is available and best suits your use case.