Thank you to @AstroSign-Dev for providing these instructions.

As builtin PHP of macOS Big Sur is PHP version 7.3 and not direct upgradeable we will install Homebrew to update PHP to version 8. To install php and neccessary development tools on macOS big Sur and above, easiest is to install git, homebrew and xcode command line tools.

How to install Homebrew and XCode command line tools »

> brew --version
> xcode-select --version

If there comes up this error during homebrew installation:

Error: An unexpected error occurred during the `brew link` step
The formula built, but is not symlinked into /usr/local
Permission denied @ dir_s_mkdir - /usr/local/Frameworks
Error: Permission denied @ dir_s_mkdir - /usr/local/Frameworks

In case of the error above you can create the /usr/local/Frameworks yourself to circumvate this error

sudo mkdir /usr/local/Frameworks
sudo chown -R $(whoami) /usr/local/Frameworks

> brew install php
> brew install git
> git --version
> php --version

This project uses tagged releases. As such, the master branch should be considered unstable and "bleeding edge".

Follow the steps to build the latest version of this extension.

cd ~ ; mkdir swephp; cd swephp;

git clone -b 4.0.4 https://github.com/cyjoelchen/php-sweph.git
cd php-sweph
phpize
./configure
make

optional:

make test

required:

For the next command you have to type in your localhost admin password to create and install the swephp.so extension into your system

sudo make install

Installing shared extensions: /usr/local/Cellar/php/8.0.9/pecl/20200930/

You need to provide your localhost admin password for this step. Check location of loaded php.ini file and extend the extension section in the php.ini file with: extension=swephp

php -i | grep php.ini
sudo nano /usr/local/etc/php/8.0/php.ini

Within nano editor I searched with Ctrl+W for extension=bz2 and then above that line I put in a new line with entry: extension=swephp

Ctrl+X to close and then Y and Enter to save the edited php.ini file

php -m | grep swephp

Now we copy some Swiss Ephemeris files of our choice to a dedicated folder on our system, and test if the extension is working

cd ~
cp ~/swephp/php-sweph/sweph/ephe/*.* ~/swephp/
nano ~/example.php

We put the below content into the just created example.php file

<?php

# Set path to ephemeris data files
swe_set_ephe_path("./swephp");

# calc planet position
list($y, $m, $d, $h, $mi, $s) = sscanf(gmdate("Y m d G i s"), "%d %d %d %d %d %d");
$jul_ut = swe_julday($y, $m, $d, ($h + $mi / 60 + $s / 3600), SE_GREG_CAL);

$planets['julday'] = $jul_ut;

for($i = SE_SUN; $i <= SE_VESTA; $i++)
{
    if ($i == SE_EARTH) continue;
    $xx = swe_calc_ut($jul_ut, $i, SEFLG_SPEED);
    if ($xx['rc'] < 0)
    { // error calling swe_calc_ut();
        $planets[$i] = array('error' => $xx['rc']);
        continue;
    }

    $planets[$i] = array(
        'name' => swe_get_planet_name($i),
        'lng' => $xx[0],
        'lat' => $xx[1],
        'speed' => $xx[3]
    );
}

$out = ['planets' => json_encode($planets, JSON_PRETTY_PRINT)];

# calc house cusps
define("GEO_LNG", 121.5);
define("GEO_LAT", 25.05);   // Taipei, Taiwan: 121E30, 25N03

$yy = swe_houses($jul_ut, GEO_LAT, GEO_LNG, "P"); // P = Placidus.

$houses = array();

for($i = 1; $i <= 12; $i ++)
{
    $houses[$i] = array('lng' => $yy['cusps'][$i]);
}

$out['houses'] = json_encode($houses, JSON_PRETTY_PRINT);

echo '<pre>';
var_dump($out);
echo '</pre>';

and execute it then with:

php ~/example.php

which should give the result of some planets and houses. We are done now with implementing swephp.so extension on a macOS Big Sur with PHP version 8

For short analysis and checking of some of our PHP calculations it may be worth to check against with command line tool swetest. As we have already installed PHP extension of Swiss Ephemeris, we have already installed all what we need on our system and need only to compile swetest and add it for easy executing to our $PATH variable.

cd ~/swephp/php-sweph/sweph/src
make
cd ~
cp ~/swephp/php-sweph/sweph/src/swetest ~/swephp/swetest
nano ~/.zshrc

Put the following line at the end of the opened file from above:

export PATH=$PATH:/Users/$USER/swephp

Activate the new $PATH variable and test swetest

. ./zshrc
swetest -edir./swephp -eswe -b16.08.2021 -geopos8.54,47.38 -fPLls -p0142536m -sid27

date (dmy) 16.8.2021 greg.   0:00:00 TT         version 2.10.02
UT:  2459442.499198167     delta t: 69.278346 sec
TT:  2459442.500000000   ayanamsa =   24° 8'10.4784 (True Citra)
geo. long 8.540000, lat 47.380000, alt 0.000000
Epsilon (m)       23°26'11.2789
Sun              119°13'31.8918  119.2255255   0.9610410
Moon             213°58'15.5311  213.9709809  14.1319143
Mars             136°40'18.4574  136.6717937   0.6334771
Mercury          133°15'15.6205  133.2543390   1.7588360
Jupiter          303°37' 4.9765  303.6180490  -0.1304109
Venus            155°38'37.7671  155.6438242   1.1826970
Saturn           285° 2'30.3615  285.0417671  -0.0708022
mean Node         42°42' 6.9441  42.7019289  -0.0529090

rm -R -f ~/swephp/php-sweph