Should I short these ground pins together?
If you need to follow FDA rules (or similar) because this is a product, then there are requirements that should be followed if the design is to be used in a product.
In many designs the MAX86150 is subject to these rules here and IEC 601-1, “Medical Electrical Equipment - Part 1: General Requirements for Safety.

Source:  https://www.analog.com/en/technical-articles/mitigation-strategies-for-ecg-design-challenges.html
It might also mean that the MAX86150 could be subject to these rules below:

The designer must examine all scenarios where current between
electrodes, or from electrodes to the circuitry or to earth ground,
could create single-fault scenarios where the current can exceed 10 µA
rms. This source/sink current is a function of frequency, but the 10
µA rms limit ranges in frequency from dc to 1 kHz. From 1 kHz to 100
kHz, the current level linearly increases with frequency: from 10 µA
rms at 1 kHz to 1 mA rms at 100 kHz. Above 100 kHz, the current is
limited to 1 mA rms.
Source: https://www.analog.com/en/technical-articles/mitigation-strategies-for-ecg-design-challenges.html

Because of these rules many designs might employ separate analog and digital grounding systems, or even isolated ones. In the datasheet it is suggested that isolated digital and analog grounds be used (I don't know how the isolation is to be maintained in the IC)

We suggest dedicated 1.8V for VDD _ANA whenever possible, otherwise
VDD_ANA is suggested to be isolated from other supplies, such as
VDD_DIG.

So they break out the grounds to give the designer options to satisfy the possible isolation requirements.
If you don't need the isolation (or separate analog and digital grounds) and the design isn't subject to these rules, then the grounds could be tied together.
One problem will be reducing noise and connecting electrodes from a circuit to another body or circuit forms a kind of AC current loop (if you've ever touched an oscilloscope and not grounded yourself you'll find the human body can be a great antenna for 60Hz). A good recommendation on isolation, separate grounds and the like is Electromagnetic Compatibility Engineering.