New results from pypsa-eur run:
In Germany, 133465841.78 MWh of biogas have been feed into the gas grid for the year 2045:
(calculated by network.links_t.p0[network.links[network.links.index.str.startswith("DE0 0 biogas to gas")].index].sum().sum()*3)

For all countries, the usage looks like this:

AL0 0 biogas 3.161167e+05
AT0 0 biogas 1.906582e+07
BA0 0 biogas 4.011812e+06
BE0 0 biogas 3.990887e+07
BG0 0 biogas 1.099119e+07
CH0 0 biogas 7.093149e+06
CZ0 0 biogas 2.473895e+07
DE0 0 biogas 1.334658e+08
DK0 0 biogas 2.631969e+06
DK1 0 biogas 9.344797e+05
EE0 0 biogas 1.525177e+06
ES0 0 biogas 6.300249e+07
ES2 0 biogas 1.654294e+06
FI1 0 biogas 1.265250e+07
FR0 0 biogas 8.509130e+07
FR6 0 biogas 1.434945e+05
GB3 0 biogas 2.596067e+07
GB4 0 biogas 7.000204e+05
GR0 0 biogas 1.118149e+07
HR0 0 biogas 2.556322e+06
HU0 0 biogas 1.796744e+07
IE4 0 biogas 1.105717e+07
IT0 0 biogas 5.975349e+07
IT5 0 biogas 1.954873e+06
LT0 0 biogas 6.741336e+06
LU0 0 biogas 1.911178e+06
LV0 0 biogas 1.944465e+05
ME0 0 biogas 3.063449e+05
MK0 0 biogas 6.616678e+05
NL0 0 biogas 6.079801e+07
NO1 0 biogas 1.061794e+08
PL0 0 biogas 6.196918e+07
PT0 0 biogas 9.156813e+06
RO0 0 biogas 2.308365e+07
RS0 0 biogas 3.940441e+06
SE1 0 biogas 8.794408e+06
SI0 0 biogas 3.804496e+06
SK0 0 biogas 1.351494e+07
XK0 0 biogas 4.075439e+05

I used this code to produce the list:
network = pypsa.Network(/path/to/pypsaeur/postnetwork/2045)
biogas_links = network.links[network.links.carrier=="biogas to gas"]
biogas_links["dispatch"] = network.links_t.p0[biogas_links.index].sum()*3
biogas_links.groupby(biogas_links.bus0).dispatch.sum()

Results for all years:

2025:
biogas 58288115 MWh
biomass 170006952 MWh
gas 842433316 MWh

2030:
biogas 58288271 MWh
biomass 561448487MWh
gas 213616374 MWh

2035:
biogas 191753884 MWh
biomass 656706909 MWh
gas 35 MWh

2045:
biogas 13346582 MWh
biomass -