Is a dedicated bandpass filter chip really neccessary for the BLE antenna of STM32WB?
It's not just a bandpass filter.   It's an antenna tuner, a &quot;transmatch&quot; or Z-match block, which performs the same task as a transformer.  (But a resonant transformer, in this case.)  It steps signal-voltage up or down, while also connecting a high impedance to a low impedance, to minimize SWR and eliminate reflected energy.  (Two coils and a capacitor form a resonant transformer, while two capacitors and a coil form a resonant Pi-network, and both topologies behave roughly the same.)
Antenna-match networks are employed whenever the antenna is too small (too short, when compared to resonant halfwave.)  At 2.4GHz and without a matching network, a groundplane antenna must be quarter-wave or ~31.25mm long, otherwise it's not receiving all the available RF signal.  The max range of your Bluetooth link would be reduced.
Ideally you'd tune it for your particular antenna and receiver, adjusting the two capacitors to maximize received signal (which maximizes the meters for linking with distant devices.)
A Z-match device performs some magic, causing the small antenna to have increased Effective Aperture EA.   This is possible because, in order to receive, an antenna must transmit:  it must emit a 180deg &quot;cancelling&quot; wave which creates an EM shadow downstream from the antenna.  The EM-energy missing from that shadow is the same as the EM energy which was absorbed by the antenna and sent to the receiver.   Or, from another viewpoint, your too-small antenna has too-high impedance when compared to the Z of free space, and this mismatch reflects incoming EM waves which you're trying to absorb.  By matching the impedance, the too-small antenna &quot;grows electrically&quot; in area, to become like a black-colored absorber-disk with diameter of 1/2-wavelength.
Z-match trivia:
Portable AM receivers use this effect to create a relatively enormous &quot;shadow,&quot; and therefore to absorb far more microwatts than expected from such a tiny antenna.  AM radios typically have a multi-element tuning capacitor, with one element connected across the loop antenna.
With mobile ham transmitters, the &quot;base load&quot; coil on your vertical whip antenna is a Z-match device, for when your antenna is shorter than quarter-wavelength.  80-meter mobile receivers don't have 40-meter antenna towers, instead they use a remote-tuned resonator at the bottom of the antenna element.)
Crystal Radios won't work unless provided with both a coil and capacitor.  Usually crystal radios are explained wrong: books claiming that the LC circuit is merely a bandpass filter, needed to eliminate undesired radio stations.  Yet if we don't provide the resonant circuit, then our crystal radio receives no signals at all (rather than receiving all stations at once.)   The resonant circuit is another of these &quot;antenna tuner&quot; devices, producing an intense local RF field, and emitting a downstream wave expected of a physically larger antenna.  (In fact, if your crystal-radio LC circuit was an infinite-Q resonator, with superconducting parts, it would behave just like a halfwave antenna.  At 550MHz, the coil in an AM radio would then intercept the same signal power as an antenna tower 140 meters tall.   See, magic!)

I would like to use an SMD chip antenna

Chip antennas were a genius idea:  employ the transmatch circuit AS AN ANTENNA.  The chip-antenna is the &quot;crystal radio&quot; of the GHz world:  a loop antenna which is far, far smaller than halfwave diameter.  By providing a parallel capacitor and adjusting to resonance, the small antenna's EA becomes large, although the sharply-resonant antenna won't be a broadband device.
I've now seen articles on &quot;beam&quot; antennas, Yagis and log-periodic, made from rows of chip-antennas  ...although that somewhat defeats the purpose, since the spacing between the &quot;antenna elements&quot; must be large.