- The Lichterfelde line (Berlin, May 1881) was the first
long-term, non-experimental electric tram line.
- Sarajevo's first electric tram was not until 1895 and is definitely
not the oldest (as claimed by the Wikipedia source cited by the OP).
- The Vevey-Montreux-Chillon tram (Switzerland, 1888) is definitely not the 2nd oldest in Europe. There are several which predate this in, for example, Austria and the UK.
This would seem to boil down to whether you count the August - September 1880 Sestroretsk / Miller's line (Fyodor Pirotsky) near St. Petersburg or not. This did carry passengers, but very few it would appear, and it only operated from the 22nd of August to sometime in September 1880. It also appears that it was at least partly experimental (see also here). Christos N. Pyrgidis, in Railway Transportation Systems: Design, Construction and Operation calls Pirotsky's effort the "first prototype of an electric tram".
If not the above, the May 1881 Lichterfelde line (Siemens & Halske) near Berlin was the first. Charles Dunbar, in Buses, Trolleys and Trams describes this as "the first public electric service" while Vukan R. Vuchic, in Urban Transit Systems and Technology calls it "the world's first electric streetcar line". According to The Siemens tram from past to present (pdf),
In the first three months of operation the tram had already carried 12,000 passengers.
Ingrid Radke-Azvedo, who lived on the street used by the tram (though not until the 1930s), also says it was "the first-ever electric streetcar in the world" in her book Out of the Rubble. The Lichterfelde line was operational until 1931.
Lichterfelde tram, photo date: 1882. Source
If Fyodor Pirotsky's line was not the first non-experimental effort, he would appear to deserve at least some credit for the Siemens & Halske tram. According to (among other sources) an 1885 US patent application, the German company had demonstrated their tram at the 1879 Berlin Trade Fair...
At the Berlin Trade Fair, 1879: the world\’s first electric railway (powered from external source), built by Siemens (image from Siemens press materials)
...but Pirotsky had been experimenting since 1875 on Miller's line (in Russia, but run by Finnish railways). Then,
In 1876, the artillery inventor [Pirotsky] published the results of experiments
in the “Engineering Journal” and sent it to many physicists and
electrical engineers. His observations and ideas pushed his colleagues
to work in this direction, and not only in Russia. A representative of
Siemens and Halske immediately sent an article to their management in
(courtesy of Google translate)
Also, after the 1879 Siemens & Halske demonstration but before their 1881 line opened,
On April 12, 1880, at the first special electrical engineering
exhibition in St. Petersburg, Pirotsky demonstrated his projects and
made a report titled “Transferring power to any distance using
galvanic current (conductors - rails and wires)”, including for train
(courtesy of Google translate)
Pirotsky, it would appear, was undone by a lack of resources in trying to get a tram line operational on a more permanent basis.
What can be said with certainty is that the 1888 Vevey-Montreux-Chillon tram was not the second in Europe; there were several others before it, among which were:
October 1883 Mödling and Hinterbrühl Tram (the first using overhead wires).
"Railcar of the first generation, 1883", Lokalbahn (tram) Mödling–Hinterbrühl. Source
February / April 1884 Frankfurt / Offenbach. This was also a Siemens project.
September 1885 Blackpool Electric Tramway, the first in the UK if one discounts more limited systems at the Crystal Palace (1882-84) and in Edinburgh (1884).
November 1887 Budapest. Plans were approved on the 1st of October and the first tram started at the end of November. Siemens & Halske were involved in the construction.