Laravel Vapor + Docker, DomPDF not rendering custom fonts, works locally, not on staging

I am having some trouble getting custom fonts working with DomPDF and Laravel Vapor. (Localy the fonts work)

These are my CSS font definitions (fonts are stored inside public/fonts)

@font-face {
            font-family: caveat;
            font-style: normal;
            font-weight: normal;
            src: url('{{ public_path('fonts/caveat.ttf') }}') format('truetype');
        }

        @font-face {
            font-family: Arial;
            font-style: normal;
            font-weight: normal;
            src: url('{{ public_path('fonts/Arial.ttf') }}') format('truetype');
        }

This is my dockerfile

FROM laravelphp/vapor:php81

RUN apk add imagemagick imagemagick-dev php81-pecl-imagick \
&& pecl install imagick \
&& docker-php-ext-enable imagick

COPY . /var/task

Locally these fonts Arial and CaveAt get rendering fine in the PDF. However after deployment to staging, the font in the PDF falls back to Helvetica

I probably need to add some commands to the dockerfile in order to get it working. My question is: What commands?

First a big thanks to the answer of VonC for his long and useful answer. It did not solve my particular issue but it's good information. I highly recommend giving it a read even if my solution works for you.

My answer is perhaps not the most recommended solution, but it works well for Laravel Vapor environments (and my specific case).

How I solved it:

fonts stored in /public/fonts

public/fonts/Arial.ttf
public/fonts/caveat.ttf

adjustments in config/dompdf.php (Works with Laravel Homestead && Serverless Vapor has a useable /tmp folder that is alive per request and can be used to write temporary files to. Creating folders within /tmp in Dockerfile does not seem to work )

    "font_dir" => '/tmp/',
    "font_cache" => '/tmp/',
    "temp_dir" => '/tmp/',

CSS font definitions

@font-face {
    font-family: caveat;
    font-style: normal;
    font-weight: normal;
    src: url('{{ asset('fonts/caveat.ttf') }}') format('truetype');
}

@font-face {
    font-family: Arial;
    font-style: normal;
    font-weight: normal;
    src: url('{{ asset('fonts/Arial.ttf') }}') format('truetype');
}

Dockerfile

FROM laravelphp/vapor:php81

RUN apk add imagemagick imagemagick-dev php81-pecl-imagick \
&& pecl install imagick \
&& docker-php-ext-enable imagick

COPY . /var/task

I cannot express how happy I was to finally see my PDF render correctly after deployment.