From NOAA's page on Geomagnetic Storms:
A geomagnetic storm is a major disturbance of Earth's magnetosphere that occurs when there is a very efficient exchange of energy from the solar wind into the space environment surrounding Earth. These storms result from variations in the solar wind that produces major changes in the currents, plasmas, and fields in Earth’s magnetosphere. The solar wind conditions that are effective for creating geomagnetic storms are sustained (for several to many hours) periods of high-speed solar wind, and most importantly, a southward directed solar wind magnetic field (opposite the direction of Earth’s field) at the dayside of the magnetosphere. This condition is effective for transferring energy from the solar wind into Earth’s magnetosphere.
The largest storms that result from these conditions are associated with solar coronal mass ejections (CMEs) where a billion tons or so of plasma from the sun, with its embedded magnetic field, arrives at Earth. CMEs typically take several days to arrive at Earth, but have been observed, for some of the most intense storms, to arrive in as short as 18 hours. Another solar wind disturbance that creates conditions favorable to geomagnetic storms is a high-speed solar wind stream (HSS). HSSs plow into the slower solar wind in front and create co-rotating interaction regions, or CIRs. These regions are often related to geomagnetic storms that while less intense than CME storms, often can deposit more energy in Earth’s magnetosphere over a longer interval.
Storms also result in intense currents in the magnetosphere, changes in the radiation belts, and changes in the ionosphere, including heating the ionosphere and upper atmosphere region called the thermosphere. In space, a ring of westward current around Earth produces magnetic disturbances on the ground. A measure of this current, the disturbance storm time (Dst) index, has been used historically to characterize the size of a geomagnetic storm. In addition, there are currents produced in the magnetosphere that follow the magnetic field, called field-aligned currents, and these connect to intense currents in the auroral ionosphere. These auroral currents, called the auroral electrojets, also produce large magnetic disturbances. Together, all of these currents, and the magnetic deviations they produce on the ground, are used to generate a planetary geomagnetic disturbance index called Kp. This index is the basis for one of the three NOAA Space Weather Scales, the Geomagnetic Storm, or G-Scale, that is used to describe space weather that can disrupt systems on Earth.
During storms, the currents in the ionosphere, as well as the energetic particles that precipitate into the ionosphere add energy in the form of heat that can increase the density and distribution of density in the upper atmosphere, causing extra drag on satellites in low-earth orbit. The local heating also creates strong horizontal variations in the in the ionospheric density that can modify the path of radio signals and create errors in the positioning information provided by GPS. While the storms create beautiful aurora, they also can disrupt navigation systems such as the Global Navigation Satellite System (GNSS) and create harmful geomagnetic induced currents (GICs) in the power grid and pipelines.
And this is from NOAA's section on Solar Flares in specific:
Solar flares are large eruptions of electromagnetic radiation from the Sun lasting from minutes to hours. The sudden outburst of electromagnetic energy travels at the speed of light, therefore any effect upon the sunlit side of Earth’s exposed outer atmosphere occurs at the same time the event is observed. The increased level of X-ray and extreme ultraviolet (EUV) radiation results in ionization in the lower layers of the ionosphere on the sunlit side of Earth. Under normal conditions, high frequency (HF) radio waves are able to support communication over long distances by refraction via the upper layers of the ionosphere. When a strong enough solar flare occurs, ionization is produced in the lower, more dense layers of the ionosphere (the D-layer), and radio waves that interact with electrons in layers lose energy due to the more frequent collisions that occur in the higher density environment of the D-layer. This can cause HF radio signals to become degraded or completely absorbed. This results in a radio blackout – the absence of HF communication, primarily impacting the 3 to 30 MHz band. The D-RAP (D-Region Absorption Prediction) product correlates flare intensity to D-layer absorption strength and spread.
I'll add a personal note here: my father was a radio engineer in the 50's and 60's, working on what was then cutting edge tech - tropospheric scatter stations - and a problem they encountered periodically was unpredictable "radio curtains" which would occur due to magnetosphere fluctuations and which would temporarily either block signal or worse, act as perfect mirrors, overwhelming the sensitive receivers with massive signal overload - so I feel like we can say that the Earth's magnetosphere has some pretty profound impacts on radio based communication not just years ago but today, based on the NOAA data.