In summary for freshwater systems, Drake et al.  aggregated contemporary estimates of CO2 and CH4 emissions from freshwater ecosystems with global estimates made by Raymond et al. , and arrived at an estimate of 3.9 PgC yr1. Rivers and streams accounted for 85% and lakes and reservoirs for 15% of the emissions . This trend will continue under scenarios of nutrient loading to inland waters over the next century where increased CH4 emission of inland water has an atmospheric impact of 1.7-2.6 PgC/ CO2-eq y-1, which is equivalent to 18-33% of annual CO2 emissions from burning fossil fuels  . For comparison, annual uptake of CO2 in land ecosystems is estimated as 3.4  PgC yr-1 . The freshwater numbers combine CO2 and CH4 and are thus not directly comparable. However, they are indicative of the importance of better accounting for freshwater systems in global carbon budgets.
IPCC
Climate Change 2022: Impacts, Adaptation and Vulnerability
IPCC Report